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.