Solving the forced Duffing equation with integral boundary conditions in the reproducing kernel space

Abstract

In this paper, we propose a new method to solve the forced Duffing equation with integral boundary conditions. Its exact solution is represented in the form of a series in the reproducing kernel space. The n-term approximation u n (x) of the exact solution u(x) is proved to converge to the exact solution. Some numerical examples are displayed to demonstrate the accuracy of the present method.

Accelerated Exponentially Fitted Operator Method for Singularly Perturbed Problems with Integral Boundary Condition

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