Generalized mapped nodal Laguerre spectral collocation method for Volterra delay integro-differential equations with noncompact kernels

• Published in: Computational & applied mathematics 2020-12, Vol.39 (4), Article 298
• Main Authors: Tang, Zhuyan, Tohidi, Emran, He, Fuli
• Format: Article
• Language: English
• Subjects: Applications of Mathematics; Applied physics; Collocation methods; Computational mathematics; Computational Mathematics and Numerical Analysis; Differential equations; Kernels; Laguerre functions; Mathematical Applications in Computer Science; Mathematical Applications in the Physical Sciences; Mathematics; Mathematics and Statistics; Robustness (mathematics); Singularity (mathematics); Spectra; Spectral methods
• ISSN: 2238-3603; 1807-0302
• DOI: 10.1007/s40314-020-01352-y

This paper is devoted to solve a class of weakly singular Volterra integro-differential equations with noncompact kernels. Since the solution of such these models may has singularities, so the classical spectral methods lose their high accuracy for solving them. Innovation of this article is that, we use the generalized mapped nodal Laguerre spectral collocation method to deal with the singularity. Therefore, we can make good use of the advantages of the mapped Laguerre functions. The best advantage of the proposed method is its robustness for solving problems that have singularity near the left (or right) boundary of the computational interval. We present the construction and analysis of the generalized log orthogonal Laguerre functions collocation method in this paper and some numerical examples with nonsmooth solutions are included to show the efficiency of the suggested numerical scheme with respect to the classical Jacobi spectral methods.