To search, Click below search items. |
| All Published Papers Search Service |
|
|
|
Title |
On the implementation of Implicit Methods to Solve Initial Values Problems for Ordinary Differential Equations |
|
Author |
Badreldin O. S. Elgabbani, Othman A. Alrusaini, Emad A. Shafie |
| Citation |
Vol. 22 No. 3 pp. 517-524 |
|
Abstract |
The study presents a new method for solving initial value problems (IVPs) for ordinary differential equations (ODEs). The study successfully satisfied Butcher conditions and got a Jacobian matrix, The study successfully satisfied Butcher conditions and got a Jacobian matrix: a11, a12, a13, a21, λ ,a23, a31, a32, ? and then applying modified Newton, to find out the unknown vector ?i from iterative equation y_i=y_i+∂_i^ . The diagonal-implicit Range-Kutta, method submitted by this study solves the problem arising from application of an implicit multistage for linear or nonlinear algebra problems.The results achieved by using these parameters via Visual studio C++, compared to the ordinary differential equations that have an exact solution are more than impressive and get a shouted result, for example while comparing the exact solution of an ordinary differential equation with our numerical solution for the same problem, we get an approximation error 9.9873D-05. Therefore, with great confidence we can use this method with problems that need numerical solution. |
|
Keywords |
Ordinary differential equation; Butcher; Runge-Kutta; implicit;, Array |
|
URL |
