JAMP  Vol.7 No.11 , November 2019
On Trigonometric Numerical Integrator for Solving First Order Ordinary Differential Equation
Abstract: In this paper, we used an interpolation function with strong trigonometric components to derive a numerical integrator that can be used for solving first order initial value problems in ordinary differential equation. This numerical integrator has been tested for desirable qualities like stability, convergence and consistency. The discrete models have been used for a numerical experiment which makes us conclude that the schemes are suitable for the solution of first order ordinary differential equation.
Cite this paper: Obayomi, A. , Ayinde, S. and Ogunmiloro, O. (2019) On Trigonometric Numerical Integrator for Solving First Order Ordinary Differential Equation. Journal of Applied Mathematics and Physics, 7, 2564-2578. doi: 10.4236/jamp.2019.711175.

[1]   Fatunla, S.O. (1988) Numerical Methods for Initial Values Problems on Ordinary Differential Equations. Academic Press, New York.

[2]   Ibijola, E.A. (2000) Some Methods of Numerical Solutions of Ordinary Differential Equations. Far East Journal of Applied Mathematics, 4, 371-390.

[3]   Partidar, K.C. (2005) On the Use of Nonstandard Finite Difference Methods. Journal of Difference Equations and Applications, 11, 735-758.

[4]   Ibijola, E.A. and Obayomi, A.A. (2012) A New Numerical Scheme for the Solution of the Logistic Equation. Advances in Differential Equations and Control Processes, 10, 1-18.

[5]   Obayomi, A.A. and Oke, M.O. (2016) Development of New Nonstandard Denominator Function for Finite Difference Schemes. Journal of Nigerian Association of Mathematical Physics, 33, 50-60.

[6]   Obayomi, A.A. (2018) Development of a Discrete Model for the Tsunami Tidal Waves. Journal of Mathematics and Computer Science, 8, 98-113.

[7]   Liu, S.J., Chen, Z.L. and Zhu, Y.P. (2015) Rational Quadratic Trigonometric Interpolation Spline for Data Visualization. Mathematical Problems in Engineering, 2015, Article ID: 983120.

[8]   Rana, S.S., Dube, M. and Tiwari, P. (2013) Rational Trigonometric Interpolation and Constrained Control of the Interpolant Curves. International Journal of Computer Applications, 67, 40-44.

[9]   Hussain, M.Z., Abbas, S. and Irshad, M, (2017) Quadratic Trigonometric B-Spline for Image Interpolation Using GA. PLoS ONE, 12, e0179721.

[10]   Mickens, R.E. (1994) Nonstandard Finite Difference Models of Differential Equations. World Scientific, 115, 144-162.

[11]   Mickens, R.E. (1981) Nonlinear Oscillations. Cambridge University Press, New York.

[12]   Anguelov, R. and Lubuma, J.M.S. (2003) Nonstandard Finite Difference Method by Nonlocal Approximation. Mathematics and Computers in Simulation, 61, 465-475.

[13]   Henrici, P. (1962) Discrete Variable Methods in ODE. John Willey & Sons, New York.

[14]   Zill, D.G. and Cullen, R.M. (2005) Differential Equations with Boundary Value Problems. 6th Edition, Cole Thompson Learning Academic Resource Center, 90-101.

[15]   Lambert, J.D. (1973) Introductory Mathematics for Scientists and Engineers. John Wiley & Sons, New York.

[16]   Dreyer, T.P. (2005) Modeling with Ordinary Differential Equations. CRC Press, Boca Raton, FL.