A finite-difference and Haar wavelets hybrid collocation technique for non-linear inverse Cauchy problems

In this research work, a finite-difference and Haar wavelet hybrid collocation scheme is introduced for the ill-posed non-linear inverse Cauchy problem with source depending on space variable along an unknown solution right side boundary. The first-order approach adopted to approximate ∂u∂t part two different series are managed ∂2u∂x2 term respectively. A simple linearization procedure used convert into linear form. contradiction various numerical schemes, current method generates well-conditioned system of algebraic equations, therefore it not required apply regularization approach. results proposed stable converge exact solution. Some tests also performed confirm accuracy, well-conditioning equations easy applicability cases.