Browsing by Author "Jafar Biazar"

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    An algorithm for choosing best shape parameter for numerical solution of partial differential equation via inverse multiquadric radial basis function
    (2020-04-30) Kazeem Issa; Sulaiman M. Hambali; Jafar Biazar
    Radial Basis Function (RBF) is a real valued function whose value rests only on the distance from some other points called a center, so that a linear combination of radial basis functions are typically used to approximate given functions or differential equations. Radial Basis Function (RBF) approximation has the ability to give an accurate approximation for large data sites which gives smooth solution for a given number of knots points; particularly, when the RBFs are scaled to the nearly flat and the shape parameter is chosen wisely. In this research work, an algorithm for solving partial differential equations is written and implemented on some selected problems, inverse multiquadric (IMQ) function was considered among other RBFs. Preference is given to the choice of shape parameter, which need to be wisely chosen. The strategy is written as an algorithm to perform number of interpolation experiments by changing the interval of the shape parameters and consequently select the best shape parameter that give small root means square error (RMSE). All the computational work has been done using Matlab. The interpolant for the selected problems and its corresponding root means square errors (RMSEs) are tabulated and plotted.
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    Numerical solution of space fractional diffusion equation using shifted Gegenbauer polynomials
    (2020-12-30) Kazeem Issa; Babatunde M. Yisa; Jafar Biazar
    This paper is concerned with numerical approach for solving space fractional diffusion equation using shifted Gegenbauer polynomials, where the fractional derivatives are expressed in Caputo sense. The properties of Gegenbauer polynomials are exploited to reduce space fractional diffusion equation to a system of ordinary differential equations, that are then solved using finite difference method. Some selected numerical simulations of space fractional diffusion equations are presented and the results are compared with the exact solution, also with the results obtained via other methods in the literature. The comparison reveals that the proposed method is reliable, effective and accurate. All the computations were carried out using Matlab package.
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    Shifted Chebyshev Approach for the Solution of Delay Fredholm and Volterra Integro-Differential Equations via Perturbed Galerkin Method
    (Azad University, Rasht, Iran, 2019-03-18) Kazeem, Issa; Jafar Biazar; Babatunde Morufu Yisa
    The main idea proposed in this paper is the perturbed shifted Chebyshev Galerkin method for the solutions of delay Fredholm and Volterra integrodifferential equations. The application of the proposed method is also extended to the solutions of integro-differential difference equations. The method is validated using some selected problems from the literature. In all the problems that are considered, the new proposed approach performs better than many other methods.