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A smooth approximation based on exponential spline solutions for nonlinear fourth order two point boundary value problems. (English) Zbl 1218.65075

Summary: Methods of order two, four and six based on exponential spline functions consisting of a polynomial part of degree three and an exponential part are developed to find approximations of linear and nonlinear fourth order two point boundary value problems. It is shown that the free parameter \(k\) of the exponential part can be used to raise the order of accuracy of the new scheme. A convergence analysis of these methods is given. Numerical examples for each the linear and the nonlinear case are included to illustrate the practical usefulness of our methods.

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
65L70 Error bounds for numerical methods for ordinary differential equations
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