×

zbMATH — the first resource for mathematics

Implicit methods for integration of initial value problems for parameterized systems of second-order ordinary differential equations. (Russian, English) Zbl 1077.65078
Zh. Vychisl. Mat. Mat. Fiz. 43, No. 11, 1684-1696 (2003); translation in Comput. Math. Math. Phys. 43, No. 11, 1620-1631 (2003).
For the numerical solution of Cauchy problems for systems of second-order ordinary differential equations the construction of simple computing algorithms of single-step integration without iterative procedures is possible. Theorems of existence and uniqueness of the solution are demonstrated. A theorem of convergence conditions for the iteration process is demonstrated. The efficiency of the offered technique is demonstrated on the numerical solution of three test problems.
MSC:
65L05 Numerical methods for initial value problems involving ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
34A30 Linear ordinary differential equations and systems
PDF BibTeX XML Cite