TY  - JOUR
AV  - none
N2  - Stiff equation is known for its rapid and slow varying time component, for which the method dedicated for this system must be capable on changing the step size depending on the varying component of the interval. This is to make sure that the computational cost can be reduced while the accuracy is preserved. In this paper, the diagonal block method derived from the family of backward differentiation formula is proposed for the direct solution of stiff Van der Pol equation. The method is implemented by varying the step size in the fixed ratios of 1, 2 and 10/19 which corresponds to constant, by halving and increasing the step respectively. The method is derived in block forms to compute the approximate solutions at two points simultaneously. By controlling the constants in its linear difference operator, the consistency of the derived method is verified. The Newton iteration technique which is derived in the block matrix form is also presented in this paper. The robustness of the proposed method is validated by solving the stiff Van der Pol equation directly and compared with the ode15s from MATLAB. Numerical results demonstrate the capability of the proposed method in solving the stiff ODEs directly. © 2023,IAENG International Journal of Computer Science. All Rights Reserved.
IS  - 1
N1  - cited By 1
TI  - Diagonal Block Method for Stiff Van der Pol Equation
ID  - scholars18770
KW  - Iterative methods
KW  -  BDF; Block methods; Computational costs; Pol equation; Step size; Stiff; Stiff equations; Time components; Van der Pol; Van der pol equation
KW  -  Numerical methods
Y1  - 2023///
PB  - International Association of Engineers
SN  - 19929978
JF  - IAENG International Journal of Applied Mathematics
A1  - Zainuddin, N.
A1  - Ibrahim, Z.B.
A1  - Zawawi, I.S.M.
UR  - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85149665069&partnerID=40&md5=a4f9e686ccee84096c558b9dba35bae5
VL  - 53
ER  -