Haar wavelet collocation method for solving hyperbolic type double interfaces problem with discontinuous coefficients

Abstract

In this article, we considered wave propagation problems through heterogeneous media or hyperbolic type interface problems. A hybrid numerical technique is presented for the numerical solution (NS) of the these type of problems. The proposed method based on Haar wavelet collocation method (HWCM) and finite difference method (FDM). In this technique, the second order spatial partial derivative is approximated by truncated Haar wavelet series and temporal derivative is approximated by FDM. In case of linear hyperbolic interface problems, the resulting algebraic systems are solved by the Gauss elimination method. While in the case of nonlinear, the nonlinearity of the problem by using quasi-Newton linearization technique. The maximum absolute errors (MAEs), root mean square errors (RMSEs) and computational convergence rate (RcN ) are calculated by utilizing distinct collocation points (CPs). The convergence and stability analysis of the proposed technique are also discussed. Both the theoretical and numerical results affirms that the approximate solution catched the exact solution very well.

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