Journal of Materials Science Research and Reviews

The Physical Application of Motion Using Single Step Block Method

Ayinde Muhammed Abdullahi

Department of Mathematics, University Abuja, Nigeria.

Ibrahim Salihu

Department of Mathematics, University Abuja, Nigeria.

Sabo John *

Department of Mathematics, Adamawa State University, Mubi 650001, Nigeria.

Silas Daniel

Department of Mathematics, Adamawa State University, Mubi 650001, Nigeria.

*Author to whom correspondence should be addressed.

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Abstract

The manuscript proposed a physical application of single step block method using the interpolation and collocation procedure for the direct solution second order physical oscillatory initial value problem. The properties of the new method which include error constant, order, zero-stability, consistency and convergent are established and satisfied. The new method was tested on some second order oscillatory initial value problems and compared with the existing works in literature, and later the new method revealed its superiority by producing less error if compared. Therefore, the new method does not required much computation when compared with predictor corrector methods.

Keywords: Physical application, single step, power series, predictor corrector, mass spring and simple harmonic motion

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References

Fatunla SO. Numerical methods for initial values problems in ordinary differential Equations. New York: Academic Press; 1988.

Lambert JD. Computational methods for ordinary differential equations. John Wiley, New York; 1973

Awoyemi DO. A class of continuous methods for general second order initial value problems in ordinary differential equations. International Journal of Computer Mathematics. 1999;72:29-37.

Skwame Y, Sabo J, Mathew M. The treatment of second order ordinary differential equations using equidistant one-step block hybrid. Asian Journal of Probability and Statistics. 2019;5(3): 1-9.

Skwame Y, Donald JZ, Kyagya TY, Sabo J. The double step hybrid linear multistep method for solving second order initial value problems. Asian Research Journal of Mathematics. 2019;15(2):1-11.

Kyagya TY, Raymond D, Sabo J. Numerical application of ordinary differential equations using power series for solving higher order initial value problems. FUW Trends in Science and Technology. 2021;6(3): 868-876.

Sabo J, Kyagya TY, Vashawa WJ. Numerical Simulation of One Step Block Method for Treatment of Second Order Forced Motions in Mass-Spring Systems. Asian Journal of Research and Reviews in Physics. 2021;5(2):1-11.

Milne WE. Numerical solution of differential equations, John Wiley and Sons; 1953.

Jator SN. A sixth order linear multistep method for the direct solution of y′′= f(x, y, y′). International Journal of Pure and Applied Mathematics. 2007;40(4):457- 472.

Henrici P. Discrete variable methods for ODE’s.John Wiley, New York; 1962.

Sabo J, Skwame Y, Kyagya TY, Kwanamu JA. The direct simulation of third order linear problems on single step block method. Asian Journal of Research in Computer Science. 2021;12(2):1-12.

Adeyeye O, Omar Z. 4-step 5 point hybrid block method for the direct solution of second order initial value problems. Journal of Mathematics and Computer science. 2017;17:527-534.

Skwame Y, Donald JZ, Kyagya TY, Sabo J. The double step hybrid linear multistep method for solving second order initial value problems. Asian Research Journal of Mathematics. 2019;15(2):1-11.

Omar Z, Adeyeye O. Solving two-second order boundary value problems using two-step block method with starting and non-starting values. International Journal of Applied Engineering Research. 2016; 11(4):2407-2410.

Ma X, Xie D, Yao L, Xie S. Extensions of single-step method for equations of motion from multi body dynamics. Mechanism and Machine Theory. 2022;177(11): 105034.

Kayode SJ, Adegboro JO. Predictor-Corrector linear multistep method for direct solution of initial value problems of second order ordinary differential equations. Asian Journal of Physical and Chemical Sciences. 2018;6(1):1-9.

Skwame Y, Bakari AI, Sunday J. Computational method for the determination of forced motions in mass-spring systems. Asian Research Journal of Mathematics. 2017;3(1):1-2.

Omole EA, Ogunware BG. 3-point single hybrid block method (3PSHBM) for direct solution of general second order initial value problem of ordinary differential equations. Journal of Scientific Research & Reports. 2018; 20(3):1-11.

Adeyefa EO, Adeniyi RB, Udoye AM, Odafi, NO. Orthogonal based zero-table numerical integrator for second order IVPs in ODEs. International Journal of Pure and Applied Mathematics. 2018;3: 329-337.

Areo EA, Rufai MA. An efficient one-eight step hybrid block method for solving second order initial value problems of ODEs. International Journal of Differential Equation and Application. 2016;15(2):117-139.