regularization method
در نشریات گروه ریاضی-
In this article, we propose an approximate technique for reconstructing a time-dependent reaction coefficient together with the surface heat flux histories and temperature distribution in a nonlinear inverse heat conduction problem (IHCP). We assume that the initial condition and the transient heat flux on the accessible boundary along with the temperature measured at specified interior locations in the domain of the problem are given as the input data. By applying the given measurements in a transformation, the main problem is reformulated as a certain parabolic problem and later a procedure based upon deploying the Ritz approximation along with the collocation method is applied which converts the problem to a nonlinear system of algebraic equations. Accurate numerical results in dealing with the exact initial and boundary data are obtained and regarding the perturbed boundary data, the regularization method based on cubic spline approximation is used, which results in obtaining stable numerical derivatives.Keywords: Inverse heat conduction, spectral technique, regularization method, operational matrix
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International Journal Of Nonlinear Analysis And Applications, Volume:12 Issue: 1, Winter-Spring 2021, PP 555 -566
The inverse problem considered in this paper is devoted to reconstruction of the unknown source term in parabolic equation from additional information which is given by measurements at final time. The cost functional is introduced and existence of the minimizer for this functional is established. The numerical algorithm to solve the inverse problem is based on the Ritz-Galerkin method with shifted Legendre polynomials as basis functions. Finally, some numerical results are presented to demonstrate the accuracy and efficiency of the proposed method for test example.
Keywords: Inverse source Problem, Cost Functional, Ill-Posed Problem, Regularization Method, Ritz-Galerkin Method -
توجه به این نکته ضرروی است که دستگاه معادلات انتگرالی ولترا-فردهلم نوع اول و دوم جز معادلات بد وضع می باشند بنابراین حل دستگاه های گسسسته شده مربوط به این معادلات دارای مشکلات فراوانی است. ما در این مقاله ابتدا یک روش منظم سازی را در نظر گرفته و مسئله نوع اول بد وضع را به یک مسئله نوع دوم خوش وضع تبدیل می کنیم. در ادامه روش عددی براساس موجک چبیشف را برای حل دستگاه خوش وضع بکار برده و همگرایی روش مربوطه را تحلیل می کنیم. در پایان چند مثال عددی با جوابهای معلوم را برای نشان دادن کارایی روش عددی پیشنهاد شده در نظر می گیریم.کلید واژگان: دستگاه مرکب معادلات انتگرالی والترا-فردهلم نوع اول و دوم، روش منظم سازی، موجک چبیشف، آنالیز همگراییIranian Journal of Numerical Analysis and Optimization, Volume:9 Issue: 1, Winter and Spring 2019, PP 127 -150 It is important to note that mixed systems of first and second-kind Volterra–Fredholm integral equations are ill-posed problems, so that solving discretized system of such problems has a lot of difficulties. We will apply the regularization method to convert this mixed system (ill-posed problem) to system of the second kind Volterra–Fredholm integral equations (well-posed problem). A numerical method based on Chebyshev wavelets is suggested for solving the obtained well-posed problem, and convergence analysis of the method is discussed. For showing efficiency of the method, some test problems, for which the exact solution is known, are considered.Keywords: Mixed systems of first, second-kind Volterra–Fredholm integral equations, Regularization method, Chebyshev wavelets, Convergence analysis
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In this paper, we propose an algorithm for numerical solving an inverse non-linear diusion problem. In additional, the least-squares method is adopted to nd the solution. To regularize the resultant ill-conditioned linear system of equations, we apply the Tikhonov regularization method to obtain the stable numerical approximation to the solution. Some numerical experiments con-rm the utility of this algorithm as the results are in good agreement with the exact data.Keywords: Inverse nonlinear diusion problem, Laplace transform, Finite dierence method, Least, squares method, Regularization method, SVD Method
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