Optimized decomposition method for solving multi-dimensional Burgers’ equation

This paper concerns the use of asymptotic expansions for the efficient solving of forward and inverse problems involving a nonlinear singularly perturbed time-dependent reaction–diffusion–advection equation. By using an asymptotic expansion with the local coordinates in the transition-layer region, we prove the existence and uniqueness of a smooth solution with a sharp transition layer for a 3D partial differential equation. Moreover, with the help of asymptotic expansion, a simplified model is derived for the corresponding inverse source problem, which is close to the original inverse problem over the entire region except for a narrow transition layer. We show that such simplification does not reduce the accuracy of the inversion results when the measurement data contain noise. Based on this simpler inversion model, an asymptotic-expansion regularization algorithm is proposed for efficiently solving the inverse source problem in the 3D case. A model problem shows the feasibility of the proposed numerical approach.

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Optimized decomposition method for solving multi-dimensional Burgers’ equation

Cited by 3 publications

References 31 publications

Effects of Noise and Fractional Derivative on the Exact Solutions of the Stochastic Conformable Fractional Fokas System

Effects of Noise and Fractional Derivative on the Exact Solutions of the Stochastic Conformable Fractional Fokas System

Analytical and numerical treatment of a nonlinear Fredholm integral equation in two dimensions

Solving forward and inverse problems involving a nonlinear three-dimensional partial differential equation via asymptotic expansions

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