Parameter identification in multidimensional hyperbolic partial differential equations using wavelet collocation method

Abstract

In this article, we have proposed a highly efficient and accurate collocation method based on Haar wavelet for the parameter identification in multidimensional hyperbolic partial differential equations (PDEs). In the proposed method, highest order derivative is represented in terms of Haar wavelet and required term of the PDE is obtained using successive integration. Due to compact support and orthogonality of Haar wavelet, this method leads to significant reduction in the computational cost. Cubic spline interpolation and Taylor series approximation are used for the parameter identification. Error analysis is carried out in order to prove the convergence of the method. The obtained numerical results and central processing unit (CPU) time ensure the efficiency and accuracy of the method.