An implicit numerical spline method for systems for ODEs. (English) Zbl 1023.65068
Summary: An implicit numerical method is introduced that gives piecewise polynomial spline approximations for the solution of an initial value problem for the equation \(y'(t)=f(t,y(t))\). Here \(f\) is a function having continuous derivatives up to the order \(r\). The method presented in this work, provides spline functions which approximate the solution of the problem in the most regular function space \(C^{r+1}\). Error estimates in \(C\) and \(C^{r+1}\) are given and the stability of the method is investigated.
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65L70 | Error bounds for numerical methods for ordinary differential equations |
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
Keywords:
error estimates; deficient spline function; implicit method; stability; stiff systems; initial value problemReferences:
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