Recovery of coefficients of a heat equation by Ritz collocation method

In this work, we discuss a one dimensional inverse problem for the heat equation where unknown functions are solely time-dependent lower order coefficient and multiplicative source term. We use as data two integral overdetermination conditions along with initial Dirichlet boundary conditions. first step, term is eliminated by applying transformation converted to an equivalent of determining conditions, well nonlocal energy over-specification. Then, propose Ritz approximation solution temperature distribution consider truncated series in source. The collocation method utilized reduce linear system algebraic equations. Since ill-posed, numerical discretization reformulated may produce ill-conditioned Therefore, Tikhonov regularization technique employed obtain stable solutions. For perturbed measurements, employ mollification derive derivatives. Numerical simulations while solving test examples presented show applicability proposed method.