Orthogonal-Based Second Order Hybrid Initial Value Problem Solver

E O Adeyefa

Abstract


This work focuses on development of an initial value problem solver by employing a new class of orthogonal polynomial, the basis function. We present the recursive formula of the class of polynomials constructed and adopt collocation technique to develop the method. The method was analyzed for its basic properties and findings show that the method is accurate and convergent.

Full Text:

PDF

References


Adeyefa, E.O. and Adeniyi, R.B. (2015) Construction of Orthogonal Basis Function and formulation of continuous hybrid schemes for the solution of third order ODEs. Journal of the Nigerian Association of Mathematical Physics, 29: 21-28.

Adeniran, A.O. and Ogundare, B.S. (2015)An efficient hybrid numerical scheme for solving general second order initial value problems (IVPs). International Journal of Applied Mathematical Research, 4(2): 411-419.

Awoyemi, D.O. (1991) A class of Continuous Linear Multistep Method for general second order initial value problems in ordinary differential equations. International Journal of Computer Mathematics, 72: 29-37.

Badmus, A.M. and Yahaya, Y.A. (2009) An Accurate Uniform Order 6 Block Method for Direct Solution of General Second Order Ordinary Differential Equations. The Pacific Journal of Science and Technology, 10(2): 248-254.

Dahlquist, G. (1979)Some properties of linear multistep and one leg method for ordinary differential equations. Department of computer science, Royal institute of technology, Stockholm.

Fatunla, S.O. (1991) Block Method for Second Order Initial Value Problem (IVP). International Journal of Computer Mathematics, 41: 55-63.

Fatunla, S.O. (1994)AClass of Block Methods for Second Order IVPs. Int. J. Comput. Math., 55: 119-133.

Golub, G.H. and Fischer B. (1992) How to generate unknown polynomials out of known orthogonal polynomials. Journal of Computational and Applied Mathematics: 43, 99 - 115.

Jator, S.N. (2007) A sixth order Linear Multistep Method for direct solution of , International Journal of Pure and Applied Mathematics, 40(1): 407-472.

Henrici, P. (1962) Discrete variable methods for ODEs. John Wiley, New York.

Lambert, J.D. (1973) Computational methods for ordinary differential equations. John Wiley, New York.

Lanczos, C. (1938) Trigonometric interpolation of empirical and analytical functions. J. Math. Physics. 17: 123 – 199.

Shampine, L.F. and Watts, H.A. (1969) Block implicit one-step methods. Journal of Computer Maths. 23:731-740.

Szego, G. (1975)Orthogonal polynomials. Amer. Math. Soc. Colloquium publications.

Tanner, L.H. (1979)The spreading of Silicone Oil Drops on Horizontal Surfaces. J. Phys. Appl. Phys. 12:1473-1484.


Refbacks

  • There are currently no refbacks.