An efficient Sinc‐collocation method by the single exponential transformation for the nonlinear fourth‐order partial integro‐differential equation with multiterm kernels. (30th November 2021)

• Record Type: Journal Article
• Authors: Jiang, Huifa; Xu, Da
• Is Part Of: Mathematical methods in the applied sciences. Volume 45:Number 5(2022)
• Page Start: 3166
• Page End: 3182
• Publication Date: 2021-11-30
• Subjects: Sinc‐collocation method -- nonlinear fourth‐order partial integro‐differential equation -- multiterm kernels -- exponential convergence; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7984
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this article, a Sinc‐collocation method is proposed and analyzed for solving the nonlinear fourth‐order partial integro‐differential equation with the multiterm kernels. The time derivative is discretized by the backward Euler method, and the Riemann–Liouville (R‐L) fractional integral terms are treated by means of the first‐order convolution quadrature. Then, the nonlinear term is linearized. A fully discrete scheme is established with the space discretization by the Sinc approximation based on the single exponential (SE) transformation. The spatial exponential convergence of the proposed method is derived. Several numerical examples are provided to illustrate the accuracy and effectiveness of our method.