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A multiquadric interpolation method for solving initial value problems. (English) Zbl 0907.65062
The authors propose a new interpolation method for the numerical solution of the initial value problem for an $$n$$th order linear ordinary differential equation. The method is based on the application of the multiquadric scheme for global interpolation of the solution and then on the collocation to obtain the equations for the unknown coefficients. The resulting system of equations is solved by using Gaussian elimination with partial pivoting. Two numerical examples which, in the authors’ opinion, show that the method under consideration offers a higher degree of accuracy than some of the known methods (in particular, such as the fourth- order Runge-Kutta method) are given.

##### MSC:
 65L05 Numerical methods for initial value problems involving ordinary differential equations 65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations 34A30 Linear ordinary differential equations and systems
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