## Convergence of the spline function for delay dynamic system.(English)Zbl 1022.65075

The convergence of $$3h$$-step spline function of degree four is studied for the solution of delay dynamic systems. It is proved that, if the local error is of order $$p$$, then the global error is of order $$p$$. Several numerical examples illustrates the convergence of the method.

### MSC:

 65L05 Numerical methods for initial value problems involving ordinary differential equations 65L20 Stability and convergence of numerical methods for ordinary differential equations 65L70 Error bounds for numerical methods for ordinary differential equations 34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
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### References:

 [1] DOI: 10.1080/00207160108805090 · Zbl 0987.65054 [2] DOI: 10.1007/BF01436181 · Zbl 0266.65056 [3] Bleyer A., Periodica Polytechnica, Tech. Univ. of Budapest Elec. Eng. 22 pp 141– (1978) [4] DOI: 10.1137/0711065 · Zbl 0307.65054 [5] El-Safty A., On numerical solution of ordinary differential equation with retarded arguments (1983) [6] DOI: 10.1007/BF01398255 · Zbl 0469.65057 [7] DOI: 10.1080/00207169008803825 · Zbl 0752.65057 [8] Loscalzo F. R., Theory and Applications of Spline Functions pp 37– (1969) · Zbl 0191.16505 [9] DOI: 10.1007/BF00281203 · Zbl 0105.30401 [10] Hale J., Theory of Functional Equations (1977) · Zbl 0352.34001 [11] Oppelstrup, J. 1976.The Rkfnb 4 Method for Delay Differential Equation, Lecture Notes in Mathematics 631 133–146. Berlin: Springer. [12] DOI: 10.1137/0708072 · Zbl 0231.65070 [13] DOI: 10.1007/BF01390178 · Zbl 0518.65053 [14] Zennaro M, ISNM 24 pp 334– (1985) [15] Shadia M., Numerical solution of delay differential and neutral differential equations using spline methods (1992)
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