Parabolic inverse problems have an important role in many branches of science and technology. The aim of this research work is to solve these classes of equations using a high order compact finite difference scheme. We consider the following inverse problem for finding u(x, t) and p(t) governed by ut = uxx + p(t)u + u(x, t) with an over specified condition inside the domain. Spatial derivatives are approximated using central difference scheme. The time advancement of the simulation is performed using a ‘‘third order compact Runge–Kutta method’’. The convergence orders for the approximation of both u and p are of o(k3 + h2) which improves the results obtained in the literature. An exact test case is used to evaluate the validity of our numerical analysis. We found that the accuracy of the results is better than that of previous works in the literature.

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