A COMPUTATIONAL ALGORITHM FOR THE NUMERICAL SOLUTION OF TWO-DIMENSIONAL TELEGRAPH INTERFACE PROBLEMS

Abstract

This paper introduces the hyperbolic two-dimensional telegraph interface model with regular interfaces, employing a hybrid numerical technique that combines Haar wavelets and the finite difference method for both linear and nonlinear problems. Spatial derivatives are approximated using truncated Haar wavelet series, while time derivatives are managed via the finite difference method. For linear problems, the Gauss elimination technique is used to solve the resulting algebraic system, whereas Newton’s quasi-linearization technique addresses nonlinearity in nonlinear problems. Performance metrics, the computation of maximum absolute errors, root mean square errors, and computational convergence rates is carried out for various configurations of collocation points demonstrating the method’s stability and accuracy, even with sharp transitions or discontinuities. Numerical experiments and analysis confirm the method’s broad applicability and precision.