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B-spline collocation for solution of two-point boundary value problems. (English) Zbl 1222.65076

The numerical solution based on B-spline collocation for boundary value problems for nonlinear differential equations up to sixth order is studied. By using the sextic B-spline collocation at the midpoints of a uniform mesh, a numerical method of order 6 is proposed. Then, an error analysis and the convergence of the method are investigated in detail. Several numerical examples, including numerical solutions for some stiff problems, are given for illustrating the efficiency of the B-spline collocation method.

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
65L70 Error bounds for numerical methods for ordinary differential equations
65L04 Numerical methods for stiff equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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