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Determination of an unknown function in a parabolic inverse problem by Sinc-collocation method

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Abstract

In this article, an inverse problem of determining an unknown time-dependent source term of a parabolic equation is considered. We change the inverse problem to a Volterra integral equation of convolution-type. By using Sinc-collocation method, the resulting integral equation is replaced by a system of linear algebraic equations. The convergence analysis is included, and it is shown that the error in the approximate solution is bounded in the infinity norm by the condition number and the norm of the inverse of the coefficient matrix multiplied by a factor that decays exponentially with the size of the system. Some examples are given to demonstrate the computational efficiency of the method. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1584–1598, 2010

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