CHEBYSHEV HYBRID MULTISTEP METHOD FOR DIRECTLY SOLVING SECOND-ORDER INITIAL AND BOUNDARY VALUE PROBLEMS

Authors

  • B. T. OLABODE DEPARTMENT OF MATHEMATICAL SCIENCES, FEDERAL UNIVERSITY OF TECHNOLOGY AKURE
  • A. L. MOMOH DEPARTMENT OF MATHEMATICAL SCIENCES, FEDERAL UNIVERSITY OF TECHNOLOGY AKURE

Abstract

A numerical method had been proposed in this work for directly solving second-order initial and boundary value problems in ordinary differential equations. The approach of collocation of a derivative function at equidistant grid and offgrid points x = xn+i/3, i = 0, 1, · · · , k, where k is the step number in the interval [xn, xn+k] was adopted. The derived Chebyshev Hybrid Multistep Method (CHMM) is of order (2k + 3). The continuous scheme was evaluated at different off-step points to obtain multiple hybrid schemes of uniform order which were solved simultaneously for dense approximations that make its computation competitive. Some numerical examples were given to demonstrate the accuracy and efficiency advantages of the proposed method.

References

E. Hairer, G. Wanner, Solving ordinary differential equations II, stiff and differential algebraic problems , second revised edition ISBN3-540-60452-9 Springer-Verlag Berlin Heidelberg New York, 241, (1996).

J. D. Lambert, Computational methods in ordinary differential equations , New York John Wiley and Sons. London. (1973).

J. D. Lambert, A.Watson, A symmetric multistep method for periodic initial value problem ,Journal of the Institute of Mathematics and its Applications 18 189-202, 1976.

J. D. Lambert, Numerical methods for ordinary differential systems: The initial value problems, John Wiley and Sons UK. 1991.

J. Butcher, The numerical analysis of ordinary differential equations:Runge-Kutta and General linear multistep methods, Wiley-Interscience, New York, 1987.

D. O. Awoyemi and O. M. Idowu, A Class of Hybrid Collocation Methods for Third Order Ordinary Differential Equations, International Journal of Computer Mathematics82 (00) 1-7, 2005.

H. Tian, Q.Yu and C. Jin, Continuous block implicit one-step methods for ordinary and delay differential equations, Applied Numerical Mathematics61 1289-1300, 2011.

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Published

2020-05-08

How to Cite

OLABODE, B. T., & MOMOH, A. L. (2020). CHEBYSHEV HYBRID MULTISTEP METHOD FOR DIRECTLY SOLVING SECOND-ORDER INITIAL AND BOUNDARY VALUE PROBLEMS. Journal of the Nigerian Mathematical Society, 39(1), 97-115. Retrieved from https://ojs.ictp.it/jnms/index.php/jnms/article/view/548

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