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

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