Non-polynomial Cubic Spline Method for Three-Dimensional Wave Equation

Abstract

The scientific community has always been showing deep concern towards partial differential equations (PDEs) and to approximate its numerical solution. This research proposes a non-polynomial cubic spline-based numerical technique for approximating the three-dimensional (3D) wave equation with Dirichlet boundary conditions. The proposed method develops an algebraic scheme for 3D wave equation which can be solved for different spatial and temporal levels. The suggested method provides a three-time level scheme with higher accuracy of order O(h8+ k8+ ?8+ ?2h2+ ?2k2+ ?2?2) by electing appropriate parameter values involved in the spline function. The stability analysis of the suggested numerical technique has been examined and numerical solution of some selected problems are included to exhibit the validity of the proposed method. Numerical results of the test problems are prepared through tables and graphs to demonstrate the effectiveness of the presented work. © 2023, The Author(s), under exclusive licence to Springer Nature India Private Limited.