A localized meshless technique for solving 2D nonlinear integro-differential equation with multi-term kernels

This paper studies an accurate localized meshless collocation approach for solving twodimensional nonlinear integro-differential equation (2D-NIDE) with multi-term kernels. The proposed strategy discretizes the unknown solution in two phases. First, the semidiscrete scheme is obtained by using backward Euler finite difference (FD) approach and the first-order convolution quadrature rule for the first order temporal derivative and the Riemann-Liouville (R-L) fractional integral, respectively. Second, the spatial discretization is established by means of the local radial basis function based on partition of unity (LRBFPU) in the space variable and its partial derivatives. Furthermore, the unconditionally stable result and first-order convergence of the time semi-discrete scheme in L2-norm are proved by the energy method. It is shown that the proposed method is accurate and that the numerical results support the theoretical analysis. (c) 2022 IMACS. Published by Elsevier B.V. All rights reserved.

Automated summary

This paper presents an accurate localized meshless collocation approach for solving a two-dimensional nonlinear integro-differential equation with multi-term kernels. The proposed strategy discretizes the unknown solution in two phases using finite difference and convolution quadrature rules. The method shows unconditional stability and first-order convergence in L2-norm, which is supported by numerical results.