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Conservation laws and the numerical solution of ODEs. (English) Zbl 0641.65057
The paper presents a method for establishing an error bound for solution by a one-step method of the initial value problem for an ordinary differential equation whose solution is required to satisfy side conditions or inequalities. It is assumed that at each step of the computation the numerical approximation to the differential equation is modified to satisfy the side conditions. The error bound then depends on the sum of the local error in the numerical approximation and magnitude of the perturbation required to satisfy the side conditions. Both of these are controlled by adjusting the step size.
Reviewer: J.B.Butler jun.

MSC:
65L05 Numerical methods for initial value problems involving ordinary differential equations
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
Software:
RKF45
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References:
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