Joshua. A. Kwanamu

• Lecturer at Adamawa State University

This paper presents a novel block hybrid method designed to improve accuracy and efficiency in solving differential equations, with specific applications in epidemiological and biological models. The new method were derived using a power series polynomial via interpolation and collocation procedure. The basic properties of the new method was analyz...

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...

Third-order problems have been found to model real-life phenomena such as thick film fluid flow, boundary layer problems, and nonlinear Genesio problems, to name a few. This research focuses on the development of an algorithm using a basis function that combines an exponential function with a power series. This algorithm, called the Exponential Fun...

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....

Over the years, the systematic search for stiff model solvers that are near-optimal has attracted the attention of many researchers. An attempt has been made in this research to formulate an implicit Four-Point Hybrid Block Integrator (FPHBI) for the simulations of some renowned rigid stiff models. The integrator is formulated by using the Lagrange...

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...

In this paper, an alternative method shall be presented for the approximation of periodic Abel's Differential Equation (ADE) of the first kind. The periodic ADE that shall be considered here are those that do not have a closed form (exact) solution (even though the solution of such equations is known to exist). First, the Theorems of shall be emplo...

Stock market prediction is the process of forecasting future prices of stocks. Stock market prediction is a challenging process as a result of uncertainties that influence the market change of price. This paper proposes a nature-inspired algorithm, called Auditory Algorithm (AA), which follows the pathway of the auditory system like that of the hum...

First order one-stage explicit Stochastic Rational Runge-Kutta methods were derived for the solution of stochastic ordinary differential equations. The derivation is based on the use of Taylor series expansion for both the deterministic and stochastic parts of the stochastic differential equation. The stability and convergence of the methods, found...

Description of circuits using differential equations is very convenient for the electrical circuits' behavioral analysis. In this paper, a one-step fifth-order computational method is proposed for the solution of second order differential equations using the Hermite polynomial as a basis function. The computational method was then applied on two re...

-Two linear multi-step schemes for the numerical solutions of initial values problems of the type ) ,,( y yxfy    by perturbed collocation using Legendre and Chebyshev polynomials as our approximating functions in tau methods of solution were developed. The schemes were found to perform very well when compared with existing known schemes and we...