Identification of time-dependent source terms and control parameters in parabolic equations from overspecified boundary data

Jaradat, Ali; Awawdeh, Fadi; Noorani, Mohd Salmi Md

doi:10.1016/j.cam.2016.09.029

Cited by 1 publication

(1 citation statement)

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“…In , the one‐dimensional forward time centered space (FTCS), one‐dimensional backward time centered space (BTCS) finite‐difference schemes and Crank–Nicolson (C–N) method have been used to solve this problem with the given data. Moreover, the optimal Homotopy analysis method (OHAM) has been used in . In Table , we compare the absolute errors of solutions for our proposed method with FTCS, BTCS, C‐N methods, and OHAM.…”

Section: Numerical Examplesmentioning

confidence: 99%

Splitting method for an inverse source problem in parabolic differential equations: Error analysis and applications

Shekarpaz

Azari

2019

Numerical Methods Partial

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In this work, we present a numerical method based on a splitting algorithm to find the solution of an inverse source problem with the integral condition. The source term is reconstructed by using the specified data and by employing the Lie splitting method, we decompose the equation into linear and nonlinear parts. Each subproblem is solved by the Fourier transform and then by combining the solutions of subproblems, the solution of the original problem is computed. Moreover, the framework of strongly continuous semigroup (or C0‐semigroup) is employed in error analysis of operator splitting method for the inverse problem. The convergence of the proposed method is also investigated and proved. Finally, some numerical examples in one, two, and three‐dimensional spaces are provided to confirm the efficiency and capability of our work compared with some other well‐known methods.

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Section: Numerical Examplesmentioning

confidence: 99%