IJCMP | A Class of Continuous Implicit Seventh-eight method for solving yâ€™= f(x, y) using power series

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A Class of Continuous Implicit Seventh-eight method for solving yâ€™= f(x, y) using power series

E. O. Omole , O. A Jeremiah , L.O. Adoghe

International Journal of Chemistry, Mathematics And Physics(IJCMP), Vol-4,Issue-3, May - June 2020, Pages 39-50 , 10.22161/ijcmp.4.3.2

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Abstract:

In this article, we develop a continuous implicit seventh-eight method using interpolation and collocation of the approximate solution for the solution of yâ€™ = f(x,y) with a constant step-size. The method uses power series as the approximate solution in the derivation of the method. The independent solution was then derived by adopting block integrator. The properties of the method was investigated and found to be zero stable, consistent and convergent. The integrator was tested on numerical examples ranging from linear problem, Prothero-Robinson Oscillatory problem, Growth Model and Sir Model. The results show that the computed solution is closer to the exact solution and also, the absolutes errors are minimal and uses lesser time for the computations.

Keywords:

Seventh-eight method, Continuous Implicit method, Power Series, yâ€™ = f(x, y), P-stable, Growth Model, SIR model, Prothero-Robinson Oscillatory problem, Convergent.

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