scholarly journals Multistep block method for solving vanishing delay differential equations

2015 ◽  
Author(s):  
Zanariah Abdul Majid ◽  
Nurul Huda Abdul Aziz
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Block Method ◽  
Vanishing Delay ◽  
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.

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