Nonmonotone Spectral Projected Gradient Methods on Convex Sets
SIAM Journal on Optimization
Numerical solution of forward and backward problem for 2-D heat conduction equation
Journal of Computational and Applied Mathematics
Solving an inverse parabolic problem by optimization from final measurement data
Journal of Computational and Applied Mathematics
A high-order exponential scheme for solving 1D unsteady convection-diffusion equations
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Error estimates for a finite element-finite volume discretization of convection-diffusion equations
Applied Numerical Mathematics
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In this paper, a new approach of the restrained optimal perturbation method is firstly proposed to study the inverse problem in the reverse process of the one-dimensional convection diffusion equation, the idea of this method is brand new that in search for the optimal perturbation value by the given initial estimate, for determining the initial distribution based on the overspecified data, and the initial estimates plus optimal perturbation value can be treated as the final initial distribution, in order to overcome the ill-posedness of this problem, a regularization term is introduced in the objective functional. Numerical examples will be given, and the results show that our method is effective.