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Notes on a new approximate solution of 2-D heat equation backward in time. (English) Zbl 1228.65186
Summary: We consider a backward heat problem that appears in many applications. This problem is ill-posed. The solution of the problem as the solution exhibits unstable dependence on the given data functions. Using a new regularization method, we regularize the problem and get some new error estimates. Some numerical tests illustrate that the proposed method is feasible and effective. This work is a generalization of many recent papers, including the earlier paper of the first two authors [Appl. Math. Comput. 215, No. 3, 873–880 (2009; Zbl 1180.65119)] and some other authors.

MSC:
65M30 Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs
35R25 Ill-posed problems for PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
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