Extended Legendre Wavelet Method for Solving Fractional Order Time Hyperbolic Partial Differential Equation

• Published in: International journal of applied and computational mathematics Vol. 9; no. 3; p. 41
• Main Authors: Gupta, Sandipan, Thakur, Bharti
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.06.2023; Springer Nature B.V
• Subjects: Applications of Mathematics; Boundary conditions; Computational Science and Engineering; Error analysis; Exact solutions; Fractional calculus; Laplace transforms; Mathematical and Computational Physics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Nuclear Energy; Operations Research/Decision Theory; Original Paper; Partial differential equations; Theoretical; Wavelet analysis; Extended Legendre wavelet; Fractional integration; Laplace transformation; Collocation method
• ISSN: 2349-5103; 2199-5796
• DOI: 10.1007/s40819-023-01512-8

An efficient numerical technique is developed for solving fractional order time hyperbolic partial differential equations by using the extended Legendre wavelet method. The fractional integral of extended Legendre wavelet in Riemann–Liouville sense is obtained by using Laplace transformation. The proposed scheme is established to compute an approximate solution and also to achieve a high degree of accuracy with a low computational cost. The solution obtained by the Extended Legendre wavelet method and standard Legendre wavelet method has been compared with their exact solution. Moreover, the convergence behavior and error analysis of the proposed method is studied through several examples.