AUTHOR KEYWORDS: error estimation; legendre wavelet basis; tau method; Weakly singular volterra integral equations INDEX KEYWORDS: Error analysis; Numerical methods, A-stable; Approximate solution; Legendre waveletss; Matrix operations; Operational tau method; Tau method; Volterra integral equations; Weakly singular, Integral equations PUBLISHER: Taylor and Francis Ltd.
In this paper, we will first study the existence and uniqueness of the solution for a one dimensional inverse heat conduction problem (IHCP) via an auxiliary problem. Then the present work is motivated by desire to obtain numerical approach for solving this IHCP. Our method begins with the utilisation of some transformations. These transformations allow us to eliminate an unknown term from parabolic equation to obtain an inverse parabolic problem with two unknown boundary conditions. To solve this inverse problem, we use the fundamental solution method. The effectiveness of the algorithm is illustrated by numerical example. Copyright 2015 Inderscience Enterprises Ltd.
AUTHOR KEYWORDS: Fundamental solution method; Inverse heat conduction problem; Stability; The L-curve method; Tikhonov regularisation method INDEX KEYWORDS: Convergence of numerical methods; Heat conduction; Problem solving, Existence and uniqueness; Fundamental solution method; Inverse heat conduction problem; L-curve methods; Numerical approaches; Parabolic Equations; Parabolic problems; Regularisation, Inverse problems PUBLISHER: Inderscience Enterprises Ltd.
AUTHOR KEYWORDS: Existence and uniqueness; stability; SVD method; the Tikhonov regularization method INDEX KEYWORDS: Efficient numerical method; Existence and uniqueness; Initial and boundary conditions; Inverse wave problems; Singular value decomposition method; SVD method; Tikhonov regularization; Tikhonov regularization method, Convergence of numerical methods; Numerical methods; Singular value decomposition, Inverse problems
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