scholarly journals Solving delay differential equations using modified 2-point block method

2013 ◽  
Author(s):  
Nurul Huda Abdul Aziz ◽  
Zanariah Abdul Majid
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Block Method ◽  
Delay Differential

scholarly journals Computation of First order Delay Differential Equations via Simpson Block Method

2020 ◽  
Vol 5 (2) ◽  
Author(s):  
Ridwanulahi I Abdulganiy ◽  
Olusheye A Akinfenwa ◽  
Osaretin E Enobabor ◽  
Blessing I Orji ◽  
Solomon A Okunuga
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Step Width ◽  
Block Method ◽  
Delay Term ◽  
First Order ◽  
Collocation Technique ◽  
Delay Differential

A family of Simpson Block Method (SBM) is proposed for the numerical integration of Delay Differential Equations (DDEs). The methods are developed through multistep collocation technique using constant step width. The convergence and accuracy of the methods are established through some standard DDEs in the reviewed literature. Keywords— Block Method, Collocation Technique, Delay Term, Delay Differential Equation, Self Starting.   

scholarly journals Numerical Approach for Solving Delay Differential Equations with Boundary Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1073
Author(s):  
Nur Tasnem Jaaffar ◽  
Zanariah Abdul Majid ◽  
Norazak Senu
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Delay Differential Equations ◽  
Numerical Solutions ◽  
Numerical Approach ◽  
Block Method ◽  
Data Simulation ◽  
Step Size ◽  
Function Calls ◽  
Delay Differential

In the present paper, a fifth-order direct multistep block method is proposed for solving the second-order Delay Differential Equations (DDEs) directly with boundary conditions using constant step size. In many life sciences applications, a delay plays an essential role in modelling natural phenomena with data simulation. Thus, an efficient numerical method is needed for the numerical treatment of time delay in the applications. The proposed direct block method computes the numerical solutions at two points concurrently at each computed step along the interval. The types of delays involved in this research are constant delay, pantograph delay, and time-dependent delay. The shooting technique is utilized to deal with the boundary conditions by applying a Newton-like method to guess the next initial values. The analysis of the proposed method based on the order, consistency, convergence, and stability of the method are discussed in detail. Four tested problems are presented to measure the efficiency of the developed direct multistep block method. The numerical simulation indicates that the proposed direct multistep block method performs better than existing methods in terms of accuracy, total function calls, and execution times.

scholarly journals Solving Delay Differential Equations of Small and Vanishing Lag Using Multistep Block Method

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Nurul Huda Abdul Aziz ◽  
Zanariah Abdul Majid ◽  
Fudziah Ismail
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Divided Difference ◽  
Interpolation Polynomial ◽  
Block Method ◽  
Step Size ◽  
Delay Term ◽  
C Program ◽  
Delay Differential ◽  
A Current

This paper considers the numerical solution of delay differential equations for solving the problem of small and vanishing lag using multistep block method. This problem arises when the size of a delay value is smaller than the step size,x-τ<h, and the delay time may even vanish whenτ→0in a current step. The proposed approach that is based on interpolation of Newton divided difference has been implemented by adapting this problem to the multistep block method. In order to achieve the required accuracy, this approach considered the appropriate degree of interpolation polynomial in approximating the solution of delay term. The developed code for solving small and vanishing lag is done using C program and we called it as DDEB5. TheP-stability andQ-stability of this method are also studied. Numerical results are presented and compared to the existing method in order to illustrate the efficiency of the proposed method.

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