A hybrid numerical algorithm for the approximation of generalized heat-like problems with constant and variable coefficients

This work aims to investigate the numerical solution of homogeneous and nonhomogeneous heat-like problems. The numerical algorithm is developed in two phases. In the first phase, the space derivatives along with solution are approximated via Haar wavelet which yield a system of ordinary differential equations (ODEs). Subsequently, the obtained system of ODEs is solved using Runge–Kutta (RK4) method. The proposed scheme is named Haar wavelet Runge Kutta (HWRK) iterative solver. The performance of the scheme is investigated by solving several benchmark models. Various error norms are computed to validate the efficiency of our proposed scheme. Moreover, we also check the computational stability and convergence. From numerical experiments, it is observed that proposed method works well for heat-like problems.