An efficient numerical method for a class of nonlinear Volterra integro-differential equations. (English) Zbl 1437.65235

Summary: We investigate an efficient numerical method for solving a class of nonlinear Volterra integro-differential equations, which is a combination of the parametric iteration method and the spectral collocation method. The implementation of the modified method is demonstrated by solving several nonlinear Volterra integro-differential equations. The results reveal that the developed method is easy to implement and avoids the additional computational work. Furthermore, the method is a promising approximate tool to solve this class of nonlinear equations and provides us with a convenient way to control and modify the convergence rate of the solution.


65R20 Numerical methods for integral equations
45J05 Integro-ordinary differential equations
45D05 Volterra integral equations
Full Text: DOI


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