Source Term and Initial Value Inversion Problem of Neumann Boundary Diffusion Equation
The source term and initial value inversion problem of diffusion equations under Neumann boundary conditions are investigated.A modified Tikhonov regularization method is proposed to address the unsuitability of this issue.A corresponding forward problem was constructed based on the given model,and the numerical solution of the forward problem was obtained using finite difference method.The corresponding inverse problem was constructed based on the forward problem and two ob-served data.The unsuitability of the inverse problem is analyzed,and under the premise of selecting appropriate regularization parameters.The error estimates between the exact and approximate solutions of the source term and initial value are derived,and relevant proofs are provided.The effectiveness of the proposed method was verified through two numerical examples.
regularized approximate solutionimproved Tikhonov regularization methoderror estimationsource terminitial value inversion problem
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