A family of numerical methods for the solution of high-order general initial value problems

1988 ◽  
Vol 67 (1) ◽  
pp. 15-25 ◽  
Author(s):  
E.H Twizell
Keyword(s):  
Numerical Methods ◽  
Initial Value Problems ◽  
High Order ◽  
Initial Value

scholarly journals A Family of High Order One-Block Methods for the Solution of Stiff Initial Value Problems

2019 ◽  
pp. 1-14
Author(s):  
I. J. Ajie ◽  
K. Utalor ◽  
P. Onumanyi
Keyword(s):  
Numerical Methods ◽  
Initial Value Problems ◽  
High Order ◽  
Numerical Implementation ◽  
Initial Value ◽  
Stiff Initial Value Problems ◽  
The Family ◽  
Block Methods ◽  
Backward Differentiation Formulas ◽  
Differentiation Formulas

In this paper, we construct a family of high order self-starting one-block numerical methods for the solution of stiff initial value problems (IVP) in ordinary differential equations (ODE). The Reversed Adams Moulton (RAM) methods, Generalized Backward Differentiation Formulas (GBDF) and Backward Differentiation Formulas (BDF) are used in the constructions. The E-transformation is applied to the triples and a family of self-starting methods are obtained. The family is for . The numerical implementation of the methods on some stiff initial value problems are reported to show the effectiveness of the methods. The computational rate of convergence tends to the theoretical order as h tends to zero.

scholarly journals New explicit high‐order one‐step methods for singular initial value problems

2020 ◽  
Author(s):  
Bohdan Datsko ◽  
Myroslaw Kutniv ◽  
Andriy Kunynets ◽  
Andrzej Włoch
Keyword(s):  
Initial Value Problems ◽  
High Order ◽  
Initial Value ◽  
One Step

scholarly journals A New Algorithm for Solving Terminal Value Problems of q-Difference Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Yong-Hong Fan ◽  
Lin-Lin Wang
Keyword(s):  
Exact Solution ◽  
Numerical Methods ◽  
Error Estimate ◽  
Numerical Solution ◽  
Numerical Method ◽  
Difference Equations ◽  
Initial Value Problems ◽  
Convergence Speed ◽  
Initial Value ◽  
Delta Derivatives

We propose a new algorithm for solving the terminal value problems on a q-difference equations. Through some transformations, the terminal value problems which contain the first- and second-order delta-derivatives have been changed into the corresponding initial value problems; then with the help of the methods developed by Liu and H. Jafari, the numerical solution has been obtained and the error estimate has also been considered for the terminal value problems. Some examples are given to illustrate the accuracy of the numerical methods we proposed. By comparing the exact solution with the numerical solution, we find that the convergence speed of this numerical method is very fast.

scholarly journals High-order nonlinear initial-value problems countably determined

2009 ◽  
Vol 228 (1) ◽  
pp. 77-82 ◽  
Author(s):  
D. Gámez ◽  
A.I. Garralda Guillem ◽  
M. Ruiz Galán
Keyword(s):  
Initial Value Problems ◽  
High Order ◽  
Initial Value
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