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A Comparative Numerical Study of Parabolic Partial Integro-Differential Equation Arising from Convection-Diffusion

Computer Modeling in Engineering & Sciences 2021年第2期126卷 673-692页

作者： Kamil Khan Arshed Ali Fazal-i-Haq Iltaf Hussain nudrat amir Department of Mathematics Islamia CollegePeshawar25000Pakistan Department of Mathematics Statistics and Computer ScienceThe University of AgriculturePeshawar25000Pakistan Department of Basic Sciences&Islamiat University of Engineering&TechnologyPeshawar25000Pakistan Department of Basic Sciences&Humanities CECOS University of Information Technology and Emerging SciencesPeshawar25000Pakistan

This article studies the development of two numerical techniques for solving convection-diffusion type partial integro-differential equation(PIDE)with a weakly singular *** trigonometric B-spline(CTBS)functions are used for interpolation in both *** first method is CTBS based collocation method which reduces the PIDE to an algebraic tridiagonal system of linear *** other method is CTBS based differential quadrature method which converts the PIDE to a system of ODEs by computing spatial derivatives as weighted sum of function *** efficient tridiagonal solver is used for the solution of the linear system obtained in the first method as well as for determination of weighting coefficients in the second *** explicit scheme is employed as time integrator to solve the system of ODEs obtained in the second *** methods are tested with three nonhomogeneous problems for their ***,computational efficiency and numerical convergence of the methods are *** of errors in approximations produced by the present methods versus different values of discretization parameters and convection-diffusion coefficients are *** and diffusion dominant cases are discussed in terms of Peclet *** results are also compared with cubic B-spline collocation method.

关键词： Partial integro-differential equation convection-diffusion collocation method differential quadrature cubic trigonometric B-spline functions weakly singular kernel

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