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The aim of the present paper is to introduce a new numerical method for solving nonlinear Volterra integro-differential equations involving delay. We apply trapezium rule to the integral involved in the equation. Further, Daftardar-Gejji and Jafari method (DGJ) is employed to solve the implicit equation. Existence-uniqueness theorem is derived for solutions of such equations and the error and convergence analysis of the proposed method is presented. We illustrate efficacy of the newly proposed method by constructing examples.
In this paper we introduce a numerical method for solving nonlinear Volterra integro-differential equations. In the first step, we apply implicit trapezium rule to discretize the integral in given equation. Further, the Daftardar-Gejji and Jafari tec
A Sinc-Nystrom method for Volterra integro-differential equations was developed by Zarebnia in 2010. The method is quite efficient in the sense that exponential convergence can be obtained even if the given problem has endpoint singularity. However,
At present, deep learning based methods are being employed to resolve the computational challenges of high-dimensional partial differential equations (PDEs). But the computation of the high order derivatives of neural networks is costly, and high ord
In this work, we present a collocation method based on the Legendre wavelet combined with the Gauss--Jacobi quadrature formula for solving a class of fractional delay-type integro-differential equations. The problem is considered with either initial
This paper presents a novel semi-analytical collocation method to solve multi-term variable-order time fractional partial differential equations (VOTFPDEs). In the proposed method it employs the Fourier series expansion for spatial discretization, wh