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12. VARIABLE STEP-SIZE TWO-STEP HYBRID METHOD FOR SOLVING SPECIAL SECOND ORDER INITIAL VALUE PROBLEMS by Y.D. Jikantoroa,c, F. Ismaila,b, Y.B. Aliyuc, A.A. Ma’alic and A. Abubakarc Volume 50 (March, 2019 Issue)
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VARIABLE STEP-SIZE TWO-STEP HYBRID METHOD FOR SOLVING

SPECIAL SECOND ORDER INITIAL VALUE PROBLEMS

Y.D. Jikantoroa,c, F. Ismaila,b, Y.B. Aliyuc, A.A. Ma’alic and A. Abubakarc

aDepartment of Mathematics, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia.

bInstitute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia.

cDepartment of Mathematics, Ibrahim Badamasi Babangida University, P.M.B 11, Lapai, Nigeria.

Abstract

We present, in this paper, a variable step-size code based on two-step hybrid methods for solving special second order initial value problems. The code consists of a third order method embedded in a fifth order method for the purpose of local error estimation, which is used in the determination of step-size of the integration. The code is then validated experimentally on a variety of test problems, where its accuracy and efficiency are obtained and compared with those of similar codes in the literature. Results obtained reveal that the proposed code is more promising. 

Numerical integration, Initial value problems, Variable step-size, Hybrid methods & Error estimation.

Mathematics Classification: 65L05.

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