Numerical methods for initial value problems in ordinary differential equations
Numerical methods for initial value problems in ordinary differential equations
Solving nonstiff higher order ODEs directly by the direct integration method
Applied Mathematics and Computation
Numerical methods for ordinary differential systems: the initial value problem
Numerical methods for ordinary differential systems: the initial value problem
Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems
Automatica (Journal of IFAC)
Variable stepsize implementation of multistep methods for y''=f(x, y, y')
Journal of Computational and Applied Mathematics - Special issue on computational and mathematical methods in science and engineering (CMMSE-2004)
International Journal of Computer Mathematics
Computers & Mathematics with Applications
A variable step implicit block multistep method for solving first-order ODEs
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Direct integrators of Runge-Kutta type for special third-order ordinary differential equations
Applied Numerical Mathematics
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This paper discusses a direct three-point implicit block multistep method for direct solution of the general third-order initial value problems of ordinary differential equations using variable step size. The method is based on a pair of explicit and implicit of Adams type formulas which are implemented in PE(CE) t mode and in order to avoid calculating divided difference and integration coefficients all the coefficients are stored in the code. The method approximates the numerical solution at three equally spaced points simultaneously. The Gauss Seidel approach is used for the implementation of the proposed method. The local truncation error of the proposed scheme is studied. Numerical examples are given to illustrate the efficiency of the method.