The solution of a parabolic differential equation with non-local boundary conditions in the reproducing kernel space

In this paper, a general technique is proposed for solving the solution of a parabolic differential equation with integral boundary condition in the reproducing kernel space. The representation of solution for the parabolic differential equation with integral boundary condition is given. The solution is given by the form of series and its approximate solution is obtained by truncating the series. Numerical results show that the method employed in the paper is valid. It is worthy to note that the method used in the paper can be generalized to solving linear ordinary or partial differential equation with initial condition and boundary conditions.

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