Sabo John

• PhD Student at Adamawa State University

This study presents a new block hybrid method aimed at solving nonlinear first-order initial value problems (IVPs). Nonlinear IVPs often appear in complex systems involving phenomena such as population dynamics, fluid flow and chemical reactions. These problems are characterized by chaotic behavior, multiple solutions and sensitivity to initial con...

This research delves into a comprehensive examination of the application and convergence analysis of a newly developed block method for simulating epidemic models. The focal point of this study revolves around the derivation and implementation of a novel scheme, crafted through the utilization of power series polynomials, ensuring the fulfilment of...

Real-world problems, particularly in the sciences and engineering, are often analyzed using differential equations to understand physical phenomena. Many situations involve rates of change of independent variables, represented by derivatives, which lead to differential equations. Solving higher-order ordinary differential equations typically involv...

The numerical application of third derivative on third order initial value problem of ordinary differential equations is consider in this paper. The method is derived by collocating and interpolating the approximate solution in power series, while Taylor series is used to generate the independent solution at selected grid and off grid points. The b...

The effective block algorithm for mathematical treatment of problematic systems of initial value problem was established and examined in this research. All the conditions are valid when examining the conditions that satisfied the properties of the scheme. The third order problematic differential equations are directly solved and relate with the sch...

The derivation of implicit one-step second derivative block method using power series for direct solution of higher order initial value problems have been developed in this research. The method was derived using interpolation and collocation procedure by introduction of off-mesh point at both grid and off-grid on linear multistep method. The analys...

Our focus in this research is to developed block method for solving higher order ordinary differential equation using power series on implicit one-step. In order to achieve the aim and objective of this research, we used interpolation, collocation and evaluate a power series approximation at some chosen grid and off-grid points to generate an impli...

This research discussed the modification of second derivative linear multistep method (LMM) using Enright's approach,which focused in solving second order ordinary differential equations (ODEs).The newly constructed method satisfied the basic requirements for the analysis of Linear Multistep methods (LMM). The methods displayed better accuracy when...

-A one-step hybrid block method for initial value problems of general second order Ordinary Differential Equations has been studied in this paper. The method is developed using interpolation and collocation techniques. The use of the power series approximate solution as an interpolation polynomial and its second derivative as a collocation equation...

In this research, we have proposed the numerical application of second derivative ordinary differential equations using power series for the direct solution of higher order initial value problems. The method was derived using power series, via interpolation and collocation procedure. The analysis of the method was studied, and it was found to be co...

In this research paper, we introduce a novel three-step block method designed to directly tackle third-order initial value problems. This method is crafted through an interpolation and collocation approach, leveraging power series analysis. We conduct a comprehensive examination of the proposed method, ensuring it meets all requisite conditions for...

In this research, we have examined the general block approach for solving higher-order oscillatory differential equations using the linear block approach (LBA). The basic properties of the new method, such as order, error constant, zero-stability, consistency, convergence, linear stability, and region of absolute stability, were also analyzed and s...

This research explores the practical implementation and simulation of oscillatory differential equations concerning objects in motion. The methodology incorporates power series polynomials, ensuring adherence to the fundamental properties of these functions. The novel approach is applied to various oscillatory differential equations, encompassing h...

This research examines the general K - step block approach for solving higher order oscillatory differential equations using Linear Block Approach (LBA). The basic properties of the new method such as order, error constant, zero-stability, consistency, convergence, linear stability and region of absolute stability were also analyzed and satisfied....

This study demonstrates the derivation of a two-step block scheme simulation through a linear block approach. The scheme's fundamental properties were thoroughly analyzed and found to fulfill all necessary conditions. The research focused on examining specific classes of oscillatory differential equations and comparing them to established methods....

This research examines the general step k − block approach for solving higher order oscillatory differential equations using Linear Block Approach (LBA). The basic properties of the new method such as order, error constant, zero-stability, consistency, convergence, linear stability and region of absolute stability were also analyzed and satisfied....

In this paper, the standard collocation approach is used to solve multi-order fractional integro-differential equations using Caputo sense. We obtain the integral form of the problem and transform it into a system of linear algebraic equations using standard collocation points. The algebraic equations are then solved using the matrix inversion meth...

An optimized half-step third derivative block scheme on testing third order initial value problems is presented in this article. This scheme suggests some certain points of evaluation which properly optimizes the truncation errors at point of formulas, the conditions that guarantee the properties of the method was considered and satisfied. However...

The numerical application of higher order linear block method for the direct solution of fourth order initial value problems was proposed using the linear block algorithm, where the methods applied in block form. The method is zero-stabile, consistent and convergent when analyzing the properties of the method. The mathematical example solved using...

The numerical application of higher order linear block method for the direct solution of fourth order initial value problems was proposed using the linear block algorithm, where the methods applied in block form. The method is zero-stabile, consistent and convergent when analyzing the properties of the method. The mathematical example solved using...

The manuscript proposed a physical application of single step block method using the interpolation and collocation procedure for the direct solution second order physical oscillatory initial value problem. The properties of the new method which include error constant, order, zero-stability, consistency and convergent are established and satisfied....

In this work, the mathematical simulation of the linear block algorithm for modeling third-order initial value problems without reduction was developed in one step. Obviously, the analysis of the method's basic properties, such as consistency, order, zero stability, error constant, and convergence, is also established in this work. When tested on s...

In this paper, the numerical solution of the ninth order boundary value problem was obtained using the modified Variational iteration method with shifted Legendre polynomials. The proposed modification involves constructing Legendre polynomials for the given boundary value problem, which are then used as the approximation's basis function. Numerica...

The introduction of new linear block method for the direct simulation of fourth order IVPs has been developed in this article. The reason for adopting direct simulation of fourth order initial value problems is to address some setbacks in reduction method. When developing the method, we adopted the linear block approach through a one step method. W...

This research showed the use of implicit single-step linear block method on third order ordinary differential equations by interpolation and collocation procedure. The block method is found using power series as a basic function through interpolation and collocation. The properties of the block method were considered. The outcome achieves on the ap...

In this research, we have proposed the simulation of linear block algorithm for modeling third order highly stiff problem without reduction to a system of first order ordinary differential equation, to address the weaknesses in reduction method. The method is derived using the linear block method through interpolation and collocation. The basic pro...

The simulation of one-step methods using interpolation and collocation for the treatment of higher order initial value problems is proposed in this paper. The new approach is derived using interpolation and collocation as a basic function through power series polynomial, where the basic properties are also analyzed. The derived method is used to tr...

In this article, the direct simulation of third order linear problems on single step block method has been proposed. In order to overcoming the setbacks in reduction method, direct method has been proposed using power series to reduce computational burden that occur in the reduction method. Numerical properties for the block method are established...

This paper discuss the numerical simulation of one step block method for treatment of second order forced motions in mass-spring systems of initial value problems. The one step block method has been developed with the introduction of off-mesh point at both grid and off- grid points using interpolation and collocation procedure to increase computati...

In this work, we developed an approximate solution of high-order integro-differential equations (IDEs.) via the third kind of Chebyshev and Hermite Polynomials as basis functions using standard collocation method for Volterra and Fredholm integro-differential equations (IDEs). An assumed approximate solution is substituted into the given problem co...

We have proposed the direct solution of high order initial value problems of ordinary differential equations on one-step third derivative block method using power series method by interpolation and collocation in this research. Numerical analysis shows that the developed method is consistent, convergence and zero stable after testing the basic prop...

We have proposed the computation of numerical method second derivative for the direct solution of higher order Initial Value Problems (IVPs) on implicit one step block method in this research. The method was derived via interpolation and collocation procedure by introduction of off-mesh point at both grid and off-grid, using the power series. The a...

The numerical applications of implicit second derivative on second order initial value problems of ordinary differential equations was studied in this paper. Special attention was given when deriving the method via interpolation and collocation procedure as a basic function, using the power series method. The analysis of the method was examined, an...

The formation of implicit second order backward difference Adam’s formulae for solving stiff systems of ODEs was study in this paper. We used interpolation and collocation in deriving backward differentiae Adam’s formulae. The basic properties of our method was analyzed, and it was found to be consistent, zero-stability and convergent, we further p...

The formation of implicit second order backward difference Adam's formulae for solving stiff systems of ODEs was study in this paper. We used interpolation and collocation in deriving backward differentiae Adam's formulae. The basic properties of our method was analyzed, and it was found to be consistent, zero-stability and convergent, we further p...

In this paper, we develop the double step hybrid linear multistep method for solving second order initial value problems via interpolation and collocation method of power series approximate solution to give a system of nonlinear equations which is solved to give a continuous hybrid linear multistep method. The continuous hybrid linear multistep met...

A general one-step hybrid block method with equidistant of order 6 has been successfully developed for the direct solution of second order IVPs in this article. Numerical analysis shows that the developed method is consistent and zero-stable which implies its convergence. The analysis of the new method is examined on two highly and mildly stiff sec...

The new accurate implicit quarter step first derivative blocks hybrid method for solving ordinary differential equations have been proposed in this paper via interpolation and collocation method for the solution of stiff ODEs. The analysis of the method was study and it was found to be consistent, convergent, zero-stability, We further compute the...

In this paper, we develop the double step hybrid linear multistep method for solving second order initial value problems via interpolation and collocation method of power series approximate solution to give a system of nonlinear equations which is solved to give a continuous hybrid linear multistep method. The continuous hybrid linear multistep met...

The new accurate implicit quarter step first derivative blocks hybrid method for solving ordinary differential equations have been proposed in this paper via interpolation and collocation method for the solution of stiff ODEs. The analysis of the method was study and it was found to be consistent, convergent, zero-stability, We further compute the...

This paper formulates an A-Stable uniform order six linear multi-step method for testing stiffly first order ordinary differential equations. Power series approximate solution was used as the basic function using interpolation and collocation techniques to derive the continuous schemes which was found to converge. The developed method is then appli...

In this research work,the construction of two-step hybrid block Simpson's methods with two, threeand four off-grid points for the solutions of first order stiff systems of ordinary differential equations (ODEs) in studied.In the derivation of the method, power series is adopted as basis function to obtain the main scheme through collocation and int...

Faldaprevir (FDV) is a potent, orally administered inhibitor of hepatitis C virus. In this single-centre, open-label, fixed-sequence, cross-over study of 32 healthy adult male and female volunteers, subjects received either a single dose of cyclosporine (CsA) 50 mg (N=16) or tacrolimus (TAC) 0.5 mg (N=16), followed by a washout of at least 14 days....

In this research work, the development of two-step implicit second derivative block methods for the solution of initial value problems of general second order ordinary differential equations is studied. In the derivation of the method, power series is adopted as basis function to obtain the main continuous scheme through collocation and interpolati...

A one-step hybrid block method for initial value problems of general second order Ordinary Differential Equations has been studied in this paper. In the derivation of the method, power series is adopted as basis function to obtain the main continuous scheme through collocation and interpolations approach. Taylor method is also used together with ne...

In this research work, a class of two-step second derivative Adam Moulton method with two off-step points for solving second order stiff ordinary differential equations is studied. The newly constructed method was applied to solve some systems of second-order stiff ordinary differential equations. From the results obtained, it was clear that the me...

Background: VERxVE data showed non-inferior virologic efficacy with extended release nevirapine (NVP-XR) dosed 400 mg once daily (QD) versus immediate release nevirapine (NVP-IR) 200 mg twice daily in a double-blind, non-inferiority study in treatment-naïve HIV-1-positive patients. Objective: To study the pharmacokinetics (PK) of the NVP formulatio...

The drug-drug interaction (DDI) potential of deleobuvir, an HCV protease inhibitor, and its two major metabolites, CD 6168 (formed via reduction by gut bacteria) and deleobuvir-AG (acyl glucuronide), was assessed in vitro. AUC (AUCi/AUC) ratios were predicted using a static model and compared to actual AUC ratios for probe substrates in a CYP450 co...

In the optional extension of clinical trial 1100.1518, 39/40 HIV-infected pediatric patients (aged 3 to <18 years) received>48 weeks of treatment with extended-release nevirapine. By last visit, all patients had undetectable viral loads and no new safety signals, demonstrating the safety and efficacy of a once-daily ARV regimen. © The Author 2015....

Patients with advanced hepatic fibrosis or cirrhosis with chronic hepatitis C virus (HCV) infection represent an unmet need. The HCV NS3/4A inhibitor, faldaprevir, was evaluated in combination with the non-nucleoside NS5B inhibitor, deleobuvir, with or without ribavirin in treatment-naïve patients with HCV genotype-1 infection in the SOUND-C2 study...

The pharmacokinetics, mass-balance and metabolism of deleobuvir, an HCV polymerase inhibitor, were assessed in healthy subjects following a single oral dose of 800 mg of [(14)C]-deleobuvir (100 μCi). The overall recovery of radioactivity was 95.2%, with 95.1% recovered from feces. Deleobuvir had moderate to high clearance and the half-life of deleo...

Faldaprevir is a potent hepatitis C virus (HCV) NS3/4A protease inhibitor. Faldaprevir is known to inhibit P-glycoprotein, CYP3A4, and UDP-glucuronosyltransferase 1A1. This study evaluated the effect of steady-state 240 mg faldaprevir on the pharmacokinetics (PK) of an oral contraceptive containing ethinylestradiol (EE) and levonorgestrel (LNG) in...

The potential inhibition of the major human cytochrome P450 (CYP) enzymes by faldaprevir was evaluated both in vitro and in clinical studies (healthy volunteers and Hepatitis C virus [HCV] genotype 1-infected patients). In vitro studies indicated that faldaprevir inhibited CYP2B6, CYP2C9, and CYP3A, and was a weak-to-moderate inactivator of CYP3A4....

Background: Faldaprevir is a potent, once-daily hepatitis C virus (HCV) NS3/4A protease inhibitor. Studies were performed to investigate potential drug interactions between faldaprevir and the commonly used antiretrovirals darunavir/ritonavir, efavirenz, and tenofovir to guide the coadministration of faldaprevir with these agents in human immunode...

To compare steady-state (ss) pharmacokinetic (PK) targets of nevirapine extended-release (NVP-XR) tablets once-daily (QD) with immediate-release (NVP-IR) tablet or oral suspension twice-daily (BID) in HIV-1 infected children and adolescents. Phase I, open-label, multi-dose, cross-over study with optional extension phase, in 85 patients 3 to <18 yea...

This study evaluated the effects of single-dose administration and steady-state concentrations of tipranavir 500 mg and ritonavir 200 mg (TPV/r) combination on the pharmacokinetics of tadalafil 10 mg (TAD) in an open-label study. Seventeen healthy male volunteers received sequential dosing of the studied product: TAD (day 1) alone in a single dose...

The use of HIV protease inhibitors (PIs) as part of antiretroviral therapy in the treatment of HIV-1 infection may be associated with an increased risk of bleeding. This prospective, randomized, open-label trial in healthy volunteers compared the effects of tipranavir/ritonavir (TPV/r), darunavir/ritonavir (DRV/r), and ritonavir (RTV) alone on plat...

This study assessed the single-dose pharmacokinetics of the herpes antiviral acyclovir (administered as the pro-drug valacyclovir) alone and in combination with twice-daily 200 mg ritonavir-boosted tipranavir (500 mg) at steady state. The study was an open label, one-sequence cross-over pharmacokinetic study in HIV-negative adults. Plasma drug conc...

The effects of tipranavir/ritonavir (TPV/r) on hepatic and intestinal P-glycoprotein (P-gp) and cytochrome P450 (CYP) enzyme activity were evaluated in 23 volunteers. The subjects received oral (p.o.) caffeine, warfarin + vitamin K, omeprazole, dextromethorphan, and midazolam and digoxin (p.o. and intravenous (i.v.)) at baseline, during the first t...

This study characterized the pharmacokinetic effects, safety, and antiretroviral activity of three different doses of the nonpeptidic protease inhibitor tipranavir, in combination with ritonavir administered twice daily for 28 days, on a number of triple-combination regimens containing a nonnucleoside reverse transcriptase inhibitor (efavirenz or n...

HIV-infected patients with opioid dependence often require opioid replacement therapy. Pharmacokinetic interactions between HIV therapy and opioid dependence treatment medications can occur.HIV-seronegative subjects stabilized on at least 3 weeks of buprenorphine/naloxone (BUP/NLX) therapy sequentially underwent baseline and steady-state pharmacoki...

Three separate controlled, two-period studies with healthy volunteers assessed the pharmacokinetic interactions between tipranavir-ritonavir (TPV/r) in a 500/200-mg dose and 500 mg of clarithromycin (CLR), 100 mg of fluconazole (FCZ), or 150 mg of rifabutin (RFB). The CLR study was conducted with 24 subjects. The geometric mean ratios (GMR) and 90%...

To identify pharmacokinetic (PK) drug-drug interactions between tipranavir-ritonavir (TPV/r) and rosuvastatin and atorvastatin, we conducted two prospective, open-label, single-arm, two-period studies. The geometric mean (GM) ratio was 1.37 (90% confidence interval [CI], 1.15 to 1.62) for the area under the concentration-time curve (AUC) for rosuva...

Previously it has been shown that tipranavir-ritonavir (TPV/r) does not affect efavirenz (EFV) plasma concentrations. This study investigates the effect of steady-state EFV on steady-state TPV/r pharmacokinetics. This was a single-center, open-label, multiple-dose study of healthy adult female and male volunteers. TPV/r 500/200 mg twice a day (BID)...

Background: Tipranavir (TPV) is a next generation protease inhibitor (PI) with potent activity against multiple PI-resistant HIV-1. This study determined the effects of steady-state TPV/r 500/200 mg bid on the pharmacokinetics (PK) of acyclovir, administered as the prodrug valacyclovir, a commonly used therapy for herpes virus infections. Methods:...

In RESIST, enfuvirtide co-administered with ritonavir-boosted tipranavir was associated with higher plasma tipranavir concentrations, which seldom rose above those associated with an increased risk of grade 3/4 transaminase elevations. Transaminase elevation rates (6.5%) and clinical hepatic event rates (5.9 events/100 person exposure years) were l...

The efficacy, safety, and pharmacokinetics of three doses of tipranavir/ritonavir (TPV/r) in highly treatment-experienced human immunodeficiency virus (HIV)-1-infected patients with protease inhibitor (PI)-resistant isolates were evaluated. A 24-week multicenter, double-blind, randomized, dose-finding trial was conducted. All patients were three-dr...

The pharmacokinetic and metabolite profiles of the antiretroviral agent tipranavir (TPV), administered with ritonavir (RTV), in nine healthy male volunteers were characterized. Subjects received 500-mg TPV capsules with 200-mg RTV capsules twice daily for 6 days. They then received a single oral dose of 551 mg of TPV containing 90 microCi of [(14)C...

Loperamide (LOP) is a peripherally acting opioid receptor agonist used for the management of chronic diarrhea through the reduction of gut motility. The lack of central opioid effects is partly due to the efflux activity of the multidrug resistance transporter P-glycoprotein (P-gp) at the blood-brain barrier. The protease inhibitors are substrates...

To characterize the steady-state pharmacokinetic combination of the nonpeptidic protease inhibitor tipranavir (TPV) with ritonavir (RTV) in 95 healthy adult volunteers, a phase 1, single-center, open-label, randomized, parallel-group trial was conducted. Participants received 250-mg self-emulsifying drug delivery system (SEDDS) capsules of TPV at d...

The purpose of this parallel treatment group, double-blind. multicenter study was to lharacterize the pharmacokinetics of nevirapine and lamivudine when coadministered to patients with the HIV-1 infection. This pharmacokinetic interaction study was nested within a larger Phase III clinical trial conducted to characterize the safety and efficacy of...

The results of two randomized, single-dose, crossover bioavailability studies are presented which describe the pharmacokinetics and oral bioavailability of nevirapine, a novel nonnucleoside antiretroviral drug. In the first study 12 healthy male volunteers received nevirapine 15 mg via short-term i.v. infusion or orally as a 50 mg tablet or referen...

The pharmacokinetics and biotransformation of the antiretroviral agent nevirapine (NVP) after autoinduction were characterized in eight healthy male volunteers. Subjects received 200-mg NVP tablets once daily for 2 weeks, followed by 200 mg twice daily for 2 weeks. Then they received a single oral dose (solution) of 50 mg containing 100 microCi of...

The results of two randomized, single-dose, crossover bioavailability studies are presented which describe the pharmacokinetics and oral bioavailability of nevirapine, a novel nonnucleoside antiretroviral drug. In the first study 12 healthy male volunteers received nevirapine 15 mg via short-term i.v. infusion or orally as a 50 mg tablet or referen...

Background Understanding antiretroviral drug interactions is a complex challenge. Phenotyping allows for a general signal of potentially important drug interactions. This is the first investigation to simultaneously evaluate TPV/r's effects on intestinal and hepatic CYP3A4/5 and P-gp under first dose and steady-state conditions.

BACKGROUND: TPV is a non-peptidic PI with potent activity against PI-resistant HIV-1 variants. TPV plasma concentrations are greatly elevated by co-administration with ritonavir (RTV). Because the liver metabolizes both TPV and RTV, we examined the effects of mild (Child-Pugh score A ≤6; CPA) and moderate hepatic impairment (Child-Pugh score B 7–9;...