The approximation for the boundary optimal control problem of Burgers-Fisher equation with constraints

This paper deals with the numerical approximation with meshless method for the boundary optimal control problem with some control and state constraints governed by the Burgers-Fisher equation, which is a nonlinear evolution equation and is the prototype model for the reaction, convection and diffusion phenomena arising in many spatial-temporal processes. By making use of the element-free Galerkin (EFG) method, the original optimal control problem is discretized spatially to a semi-discrete optimal control problem governed by a system of nonlinear ordinary differential equations. Then, by using the control parameterization method, the original problem can be reduced to an optimal parameter selection problem governed by a lumped parameter system, which can be solved as a nonlinear optimization problems by using the Sequential Quadratic Programming (SQP) algorithm. The numerical simulations are given to illustrate the effectiveness of the proposed numerical approximation method.

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