Hybrid Haar wavelet and meshfree methods for hyperbolic double interface problems: Numerical implementations and comparative performance analysis

Abstract

This paper introduces a variety of approaches for solving 2D and 3D hyperbolic double interface problems. The methods are based on the Haar wavelet method, multiquadric radial basis function method, and integrated multiquadric radial basis function method. Temporal derivatives are handled using the second central difference and the Houbolt method. Various numerical approaches based on these methods are developed, and their implementations are discussed in complete detail. The paper evaluates and compares the performances of these approaches using both linear and nonlinear 2D and 3D double interface hyperbolic problems. Error analysis, conducted using the L-infinity norm, and efficiency assessments measured through CPU times contribute to a comprehensive understanding of the applicability and comparative effectiveness of the proposed methods. This study provides valuable insights for researchers and practitioners dealing with the challenges posed by interface problems in general.