New Spectral Second Kind Chebyshev Wavelets Scheme for Solving Systems of Integro-Differential Equations

In this paper, a spectral scheme based on shifted second kind Chebyshev wavelets collocation method (S2CWCM) is introduced and used for solving systems of integro-differential equations. The main idea for obtaining spectral numerical solutions of these equations is essentially developed by reducing the linear or nonlinear equations with their initial conditions to a system of linear or nonlinear algebraic equations in the unknown expansion coefficients. Convergence analysis and some illustrative examples included, to demonstrate the validity and the applicability of the method. Numerical results obtained are compared favorably with the analytical known solutions. © 2016, Springer India Pvt. Ltd.