A new Jacobi wavelets decomposition method for solving partial differential equations

Purpose The paper proposes a new spectral method based on Jacobi wavelets for numerically solving partial differential equations (PDEs). Design/methodology/approach The authors used Jacobi wavelets as basis functions and employed the operational matrix of derivative to reduce PDEs to systems of ordinary differential equations (ODEs). A dedicated software package was developed to implement the proposed algorithm. Findings The authors presented several numerical examples to demonstrate the accuracy and efficiency of the proposed method in solving various types of PDEs. Originality/value The method is original in its use of Jacobi wavelets for constructing a wavelet-based spectral method applicable to PDEs.