scholarly journals Extended one-step block method for solving stiff initial value problem

2015 ◽  
Author(s):  
Nur Zahidah Mukhtar ◽  
Zanariah Abdul Majid
Keyword(s):  
Initial Value Problem ◽  
Block Method ◽  
Initial Value ◽  
One Step

scholarly journals Hybrid Third Derivative Block Method for the Solution of General Second Order Initial Value Problems with Generalized One Step Point

2019 ◽  
Vol 12 (3) ◽  
pp. 1199-1214
Author(s):  
Ra'ft Abdelrahim ◽  
Z. Omar ◽  
O. Ala’yed ◽  
B. Batiha
Keyword(s):  
Power Series ◽  
Convergence Analysis ◽  
Initial Value Problem ◽  
Initial Value Problems ◽  
Numerical Procedure ◽  
Second Order ◽  
Block Method ◽  
Initial Value ◽  
One Step ◽  
Third Derivative

This paper deals with two-step hybrid block method with one generalized off-step points for solving second order initial value problem. In derivation of this method, power series of order nine are interpolated at the first two step points while its second and third derivatives are collocated at all point in the selected interval. The new developed method is employed to solve several problems of second order initial value problems. Convergence analysis of the new method alongside numerical procedure is established. The performance of the proposed method is found to be more accurate than existing method available in the literature when solving the same problems.

scholarly journals The Treatment of Second Order Ordinary Differential Equations Using Equidistant One-step Block Hybrid

2019 ◽  
pp. 1-9
Author(s):  
Y. Skwame ◽  
J. Sabo ◽  
M. Mathew
Keyword(s):  
Numerical Analysis ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Value Problems ◽  
Second Order ◽  
Direct Solution ◽  
Block Method ◽  
Initial Value ◽  
One Step ◽  
Better Than

A general one-step hybrid block method with equidistant of order 6 has been successfully developed for the direct solution of second order IVPs in this article. Numerical analysis shows that the developed method is consistent and zero-stable which implies its convergence. The analysis of the new method is examined on two highly and mildly stiff second-order initial value problems to illustrate the efficiency of the method. It is obvious that our method performs better than the existing method within which we compare our result with. Hence, the approach is an adequate one for solving special second order IVPs.

scholarly journals Numerical Simulation of One Step Block Method for Treatment of Second Order Forced Motions in Mass-Spring Systems

2021 ◽  
pp. 1-11
Author(s):  
J. Sabo ◽  
T. Y. Kyagya ◽  
W. J. Vashawa
Keyword(s):  
Numerical Simulation ◽  
Initial Value Problems ◽  
Second Order ◽  
Block Method ◽  
Initial Value ◽  
Mathematical Problems ◽  
One Step ◽  
Grid Points ◽  
The One ◽  
Mass Spring

This paper discuss the numerical simulation of one step block method for treatment of second order forced motions in mass-spring systems of initial value problems. The one step block method has been developed with the introduction of off-mesh point at both grid and off- grid points using interpolation and collocation procedure to increase computational burden which may jeopardize the accuracy of the method in terms of error. The basic properties of the one step block method was established and numerical analysis shown that the one step block method was found to be consistent, convergent and zero-stable. The one step block method was simulated on three highly stiff mathematical problems to validate the accuracy of the block method without reduction, and obviously the results shown are more accurate over the existing method in literature.

scholarly journals One–Step Hybrid Block Scheme for the Numerical Approximation for Solution of Third Order Initial Value Problems

2021 ◽  
pp. 51-61
Author(s):  
J. Sabo ◽  
T. Y. Kyagya ◽  
M. Solomon
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Value Problems ◽  
Block Method ◽  
Initial Value ◽  
Third Order ◽  
First Order ◽  
Block Algorithm ◽  
One Step ◽  
Linear Block

In this research, we have proposed the simulation of linear block algorithm for modeling third order highly stiff problem without reduction to a system of first order ordinary differential equation, to address the weaknesses in reduction method. The method is derived using the linear block method through interpolation and collocation. The basic properties of the block method were recovered and was found to be consistent, convergent and zero-stability. The new block method is been applied to model third order initial value problems of ordinary differential equations without reducing the equations to their equivalent systems of first order ordinary differential equations. The result obtained on the process on some sampled modeled third order linear problems give better approximation than the existing methods which we compared our result with.

THREE POINTS BLOCK EMBEDDED DIAGONALLY IMPLICIT RUNGE-KUTTA METHOD FOR SOLVING ODES

2021 ◽  
Vol 10 (11) ◽  
pp. 3449-3460
Author(s):  
Y.F. Rahim ◽  
M.E.H. Hafidzuddin
Keyword(s):  
Initial Value Problem ◽  
Numerical Results ◽  
Kutta Method ◽  
Initial Value ◽  
Stiff System ◽  
The Third ◽  
Runge Kutta Method ◽  
One Step ◽  
Runge Kutta

Block Embedded Diagonally Implicit Runge-Kutta (BEDIRK4(3)) me- thod derived using Butcher analysis and equi-distribution of error approach is outperformed standard Runge-Kutta (RK) formulae. BEDIRK4(3) method produces approximation to the solution of initial value problem (IVP) at a block of three points simultaneously. The standard one step RK3(2) method is used to approximate the solution at the first point of the block. At the second points the solution is approximated using RK4(2) method which is generated by the previous research. The same approach is used to obtain the solution at the third point. The code for this method was built and the algorithm developed is suitable for solving stiff system. The efficiency of the method is supported by some numerical results.

Sign in / Sign up

Export Citation Format

Share Document