Numerical Approach for Solving Delay Differential Equations with Boundary Conditions

Mathematics

Zanariah Abdul Majid¹  NurTasnem Jaaffar¹  Norazak Senu¹ 

[1] Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400, Selangor, Malaysia;

关键词: delay differential equations;    boundary value problems;    linear multistep method;    numerical simulation;    block method;   

DOI  :  10.3390/math8071073

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown