Haar Wavelet based method of lines for the numerical solutions of inverse problems with space dependent source and noise intensity parameter on the boundary

Abstract This paper studies, the numerical solutions of (1+1)- and (1+2)- dimensional type problems with space-dependent heat sources. In the proposed solution strategy, the spatial part is estimated using the Haar wavelet, and the temporal part is tackled using the Runge-Kutta method of order four (RK4). Numerical results of different types of benchmark test problems are presented. The Obtained results are compared with the existing state-of-art algorithms and with the exact solution. The computational stability and accuracy of the proposed solution strategy are also discussed. We conclude from numerical experiments that the proposed hybrid method is an efficient and reliable way to deal with the inverse type partial differential equations which arise in different scientific and engineering disciplines.