Introduction to numerical analysis: 2nd edition
Introduction to numerical analysis: 2nd edition
Error Bounds for the Runge-Kutta Single-Step Integration Process
Journal of the ACM (JACM)
A Generalization of a Theorem of Carr on Error Bounds for Rung-Kutta Procedures
Journal of the ACM (JACM)
Pseudo-Runge-Kutta Methods of the Fifth Order
Journal of the ACM (JACM)
Parameters for pseudo Runge-Kutta methods
Communications of the ACM
A new class of methods for solving ordinary differential equations
ICCMSE '03 Proceedings of the international conference on Computational methods in sciences and engineering
Rooted tree analysis of Runge-Kutta methods with exact treatment of linear terms
Journal of Computational and Applied Mathematics
ARK methods: some recent developments
Journal of Computational and Applied Mathematics - Special issue: Selected papers of the international conference on computational methods in sciences and engineering (ICCMSE-2003)
Nordsieck representation of two-step Runge-Kutta methods for ordinary differential equations
Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
Error estimate of a fourth-order Runge-Kutta method with only one initial derivative evaluation
AFIPS '68 (Spring) Proceedings of the April 30--May 2, 1968, spring joint computer conference
Nordsieck representation of two-step Runge--Kutta methods for ordinary differential equations
Applied Numerical Mathematics
Rooted tree analysis of Runge-Kutta methods with exact treatment of linear terms
Journal of Computational and Applied Mathematics
ARK methods: some recent developments
Journal of Computational and Applied Mathematics - Special issue: Selected papers of the international conference on computational methods in sciences and engineering (ICCMSE-2003)
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A third order two step method and a fourth order two step method for the numerical solution of the vector initial value problem dy ÷ dx=F(y), y(a) = n can be defined by making evaluations of F similar to those found in a classical Runge-Kutta formula. These two step methods are different from classical Runge-Kutta methods in that evaluations of F made at the previous point are used along with those made at the current point in order to obtain the solution at the next point. If the stepsize is fixed, this use of previous computations makes it possible to obtain the solution at the next point by evaluating F two or three times for the third or fourth order method, respectively.These methods are consistent with the initial value problem and are shown to be convergent with its unique solution under certain restrictions. The local truncation error terms are given. Finally, a few numerical results are presented.