Jabar Hassan

College of Scinece Salahaddin University - Erbil Erbil

In this work, we investigate stability of solutions relative to the driver to a general class of nonlinear integral equations in two dimensions in binary reproducing kernel Hilbert space. Next, we analyze estimate error of solutions in terms of uniform grid numbers of compact subintervals of [a, b] × [c, d]. In addition, we use the reproducing kern...

In this research, we study stability of solutions with respect to the driver of a system of nonlinear Volterrs integral equations in reproducing Kernel Hilbert space. We study error estimate of solutions in terms of uniform grid numbers of subintervals of [a, b]. Furthermore, we use the reproducing kernel method to approximate the solutions of the...

We use the contraction mapping theorem to present the existence and uniqueness of solutions in a short time to a system of non-linear Volterra integral equations in a certain type of direct-sum H[a; b] of a Hilbert space V[a; b]. We extend the local existence and uniqueness of solutions to the global existence and uniqueness of solutions to the pro...

We introduce new reproducing kernel Hilbert spaces on a trapezoidal semi‐infinite domain B∞ in the plane. We establish uniform approximation results in terms of the number of nodes on compact subsets of B∞ for solutions to nonhomogeneous hyperbolic partial differential equations in one of these spaces, W˜(B∞). Furthermore, we demonstrate the stabil...

We introduce new reproducing kernel Hilbert spaces on a semi‐infinite domain and demonstrate existence and uniqueness of solutions to the nonhomogeneous telegraph equation in these spaces if the driver is square‐integrable and sufficiently smooth.

Among the PMHS test series available in the literature, four dynamic test configurations were chosen to assess the biofidelity of the lower leg. 1. Axial impact against the foot-leg-knee complex: the test series of Funk et al. (2000) was used. The load measured in the tibia shaft as a function of the footplate displacement was chosen as response re...

In this paper we are concerned with an approximate method to solve Cauchy-type singular integral equations (CSIEs). The mechanism of this method is based on an approximation of the unknown function which can be done by appropriate finite series. Galerkin method has been used to build a system of linear equations which leads to determine the unknown...