The Direct Simulation of Third Order Linear Problems on Single Step Block Method
Asian Journal of Research in Computer Science,
In this article, the direct simulation of third order linear problems on single step block method has been proposed. In order to overcoming the setbacks in reduction method, direct method has been proposed using power series to reduce computational burden that occur in the reduction method. Numerical properties for the block method are established and the method developed is consistent, convergent and zero-stable. To validate the accuracy of the block method, certain numerical test problems were considered, the results shown that the accuracy of our method are more accurate over the existing method in literature.
- Direct method
- computational burden
- linear problems
- reduction method
- single step
- third order
How to Cite
Spiegel RM. Theory and problems of advance mathematics for engineers and scientist, McGraw Hill, Inc. New York; 1971.
Lambert JD. Computational methods in ordinary differential equations. Introductory Mathematics for Scientists and Engineers. Wiley; 1973.
Fatunla SO. Numerical methods for initial value problems in ordinary differential equations. Academic press inc. Harcourt Brace Jovanovich Publishers, New York; 1988.
Sarafyan D. New algorithms for the continuous approximate solutions of ordinary differential equations and the upgrading of the order of the processes. Computers & Mathematics with Applications. 1990;20(1):77-100.
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(1):29-37.
Dahlquist G. Convergence and stability in the numerical integration of ordinary differential equations. Mathematica Scandinavia. 1959;4:33-53.
Hall G, Suleiman MB. Stability of Adams-type formulae for second order ordinary differential equations. IMA Journal of Numerical Analysis. 1981;1(4):427-438.
Omar Z. Developing parallel 3-point implicit block method for solving second order ordinary differential equations directly. IJMS. 2004;11(1):91-103.
Kayode SJ. A class of maximal order linear multistep collocation methods for direct solution of ordinary differential equations. Unpublished doctoral dissertation, Federal University of Technology, Akure, Nigeria; 2004.
Adeyeye O, Omar Z. Direct solution of initial and boundary value problem of third order ODEs using maximum-order fourth-derivative block method. 4th Innovation and Analytics Conference & Exhibition. AIP Conf. Proc. 2019a;2138:030002-1-03002-6.
Adeyeye O, Omar Z. Solving third order ordinary differential equation using one-step block method with four equidistance generalized hybrid points. International Journal of Applied Mathematics. 2019b;49(2):1-9.
Kuboye JO, Elusakin OR, Quadri OF. Numerical algorithms for direct solution of fourth order ordinary differential equations. J. Nig. Soc. Phys. Sci. 2020;2:218-227.
Raymond D, Skwame Y, Adiku L. Four step one hybrid block methods for solution of fourth derivative ordinary differential equations. Journal of Advances in Mathematics and Computer Science. 2021;36(3):1-10.
Sabo J, Althemai JM, Hamadina M. The computation of numerical method second derivative for the direct solution of higher order initial value problems. Dutse Journal of Pure and Applied Sciences. 2021;7(2a):110-121.
Abdelrahim R. Four step hybrid block method for the direct solution of fourth order ordinary differential equations. Int. J. Anal. Appl. 2021;12(1):215-229.
Tumba P, Skwame Y, Raymond D. Half-step implicit linear hybrid block approach of order four for solving third order ordinary differential equations. Dutse Journal of Pure and Applied Sciences (DUJOPAS). 2021;7(2b):124-133.
Omar Z. Parallel block methods for solving higher order ordinary differential equations directly. PhD. Thesis, Universiti Putra Malaysia (unpublished); 1999.
Adoghe LO, Omole EO. A fifth-fourth continuous block implicit hybrid methodfor the solution of third order initial value problems in ordinary differential equations. Applied and Computational Mathematics. 2019;8(3):50-57.
Aigbiremhom AA, Omole EO. A four-step collocation procedure by means of perturbation term with application to third-order ordinary differential equation. International journal of computer Applications. 2020;175(24):25-36.
Taparki RM, Gurah D, Simon S. An implicit Runge-Kutta method for solution of third order initial value problem in ODE. International Journal of Numerical Mathematics. 2010;6:174-189.
Skwame J, Dalatu PI, Sabo J, Mathew M. Numerical application of third derivative hybrid block methods on third Order Initial Value Problem of ordinary differential equations. IJSAM. 2019;4(6):90-100.
Kuboye JO, Omar Z. The numerical computation of block method for direct solution of third order ordinary differential equations. International Journal of Mathematics and Computers in Simulation. 2016;10:133-141.
Areo EA, Omojola MT. One-twelveth step continuous block method for the solution of y′′′ = f(x, y, y′, y′′). International Journal of Pure and Applied Mathematics. 2017;114(2):165-178.
Adeyeye O, Omar Z. New self-starting approach for solving special third order initial value problems. Int. J. Pure Appl. Math. 2018;118(3):511-517.
Abstract View: 38 times
PDF Download: 16 times