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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:
65L10Boundary value problems for ODE (numerical methods)
65L12Finite difference methods for ODE (numerical methods)
65L20Stability and convergence of numerical methods for ODE
34B05Linear boundary value problems for ODE
34B15Nonlinear boundary value problems for ODE
65L70Error bounds (numerical methods for ODE)
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