A class of exponentially fitted second derivative extended backward differentiation formula for solving stiff problems

• Autorzy: Ehigie J O , Okunuga S A , Sofoluwe A B
• Języki publikacji: EN

Abstrakty

EN

An exponentially fitted second derivative extended backward differentiation formula (SDEBDF) is derived from the class of composite, multiderivative linear multistep method with a free parameter to allow for the exponential fitting. Some numerical properties such as stability of the methods are investigated as a pair of predictor-corrector (P-C) technique based on a proposed algorithm, to which the local error estimates are also obtained. The efficiency of the new method tested on some standard prob- lems shows that the method compares favourably with existing methods and with high accuracy.

Słowa kluczowe

EN

exponential fitted; second derivative; backward differentiation formula; stability

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2013
• Tom: Nr 51
• Strony: 71--84
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Ehigie J O

• Department of Mathematics University of Lagos, Nigeria

autor

Okunuga S A

• Department of Mathematics University of Lagos, Nigeria

autor

Sofoluwe A B

• Department of Computer Sciences University of Lagos, Nigeria

Bibliografia

• [1] Abhulimen C.E., An exponentially fitted Predictor-Corrector formula for stiff system of Ordinary Differential Equations, Intenational Journal of Com- putational and Applied Mathematics, 4(2)(2009), 115-126.
• [2] Abhulimen C.E., Okunuga, Exponentially fitted second derivative multistep methods for stiff initial value problems in rdinary differential equations, Intenational Journal of Computational and Applied Mathematics, 4(2)(2008), 115-126.
• [3] Abhulimen C.E., Otunta F.O., A new class of exponential fitting for initial value problems in ordinary differemtial equations, J. of Nig. Math. Soc., 28(2009), 13-28, 982-983.
• [4] Akinfenwa O., Jator S., Yoa N., Eight order backward differentiation formula with continuous coefficients for stiff ordinary differential equations, World Academy of Science, Engineering and Technology, 74(2011), 848-853.
• [5] Cash J.R., On the integration of stiff systems of ordinary differential equations using extended backward differentiation formula, Numer. Math., 3(1980), 235-246.
• [6] Cash J.R., On the exponential fitting of composite, multiderivate liinear multistep methods, SIAM J. Numer. Anal., 18(5)(1981), 808-821.
• [7] Cash J.R., Second Derivative Extended Backward Differentiation Formulas for the Numerical Solution of stiff Systems, SIAM J. Numer. Anal., 18(1981), 21 - 36.
• [8] Curtiss C.F., Hirsohfelder J.O., Integration of stiff equations, Proc. Nat. Acad. Sci., 38(1952), 235 - 243.
• [9] Enright W.H., Second derivative multistep methods for stiff ordinary differential equations, SIAM Journal of Numerical Analysis, 11(2)(1974), 321-331.
• [10] Enright W.H., Pryoe J.D., Two Fortran Packages for Assessing IV methods, Technical Report 83(16), Department of Computer Science, University of Toronto, Canada, 1983.
• [11] Gear C.W., Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, New Jersey, 1971.
• [12] Hairer E., Wanner G., Solving Ordinary Differential Equations II: Stiff and Differential Algebraic Problems, Second Revised Edition, Springer Verlag, Germany, 1996.
• [13] Jackson L.W., Kenue S.K., A fourth-order exponentially fitted method, SIAM J. Numer. Anal., 11(1974), 965-978.
• [14] Lambert J.D., Computational methods in Ordinary Differential Equations, John Wiley and sons, New York, 1973.
• [15] Lambert J.D., Numerical Methods for Ordinary Differential Systems, John Wiley and sons, New York, 1991.
• [16] Liniger W., Willoughby R.A., Efficient integration methods for stiff systems of ordinary differential equations, SIAM J. Numer Anal, 7(1970), 47-65.
• [17] Okunuga S.A., Composite Multiderivative method for Solving Stiff IVPs, Ph.D Thesis, University of Lagos, Nigeria, 1992.
• [18] Okunuga S.A., A fourth order composite two-step method for Stiff problems, Int. J. of Computer Mathematics, 72(1)(1999), 39-47.