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Du, Juan; Cui, Minggen

Solving the forced Duffing equation with integral boundary conditions in the reproducing kernel space. (English) Zbl 1213.65106

Int. J. Comput. Math. 87, No. 9, 2088-2100 (2010).
The authors propose a new method to solve the forced Duffing equation with integral boundary conditions. The idea is to construct the numerical solution by an iterative scheme in the corresponding reproducing kernel space. Then, uniform convergence towards the exact solution is shown. Some examples based on linear and nonlinear second-order equations are provided to demonstrate the efficiency and robustness of the method.
Reviewer: Johannes Schropp (Konstanz)

Cited in 13 Documents

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
42B05 Fourier series and coefficients in several variables
46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
47B32 Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces)

Keywords:

forced Duffing equation; integral boundary condition; reproducing kernel space; exact solution; iterative sequence

Software:

Matlab
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\textit{J. Du} and \textit{M. Cui}, Int. J. Comput. Math. 87, No. 9, 2088--2100 (2010; Zbl 1213.65106)
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