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**A variable step implicit block multistep method for solving first-order ODEs.**
*(English)*
Zbl 1183.65094

Summary: A new four-point implicit block multistep method is developed for solving systems of first-order ordinary differential equations (ODEs) with variable step size. The method computes the numerical solution at four equally spaced points simultaneously. The stability of the proposed method is investigated. The Gauss-Seidel approach is used for the implementation of the proposed method in the \(PE(CE)^m\) mode. The method is presented in a simple form of Adams type and all coefficients are stored in the code in order to avoid the calculation of divided difference and integration coefficients. Numerical examples are given to illustrate the efficiency of the proposed method.

### MSC:

65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |

65L05 | Numerical methods for initial value problems involving ordinary differential equations |

34A34 | Nonlinear ordinary differential equations and systems |

65L50 | Mesh generation, refinement, and adaptive methods for ordinary differential equations |

65L20 | Stability and convergence of numerical methods for ordinary differential equations |

### Keywords:

variable step size; ordinary differential equations; Adams-type method; four-point implicit block multistep method; stability Gauss-Seidel approach; divided difference; numerical examples
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XMLCite

\textit{S. Mehrkanoon} et al., J. Comput. Appl. Math. 233, No. 9, 2387--2394 (2010; Zbl 1183.65094)

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DOI

### References:

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