ON SHOOTING AND FINITE DIFFERENCE METHODS FOR NON-LINEAR TWO POINT BOUNDARY VALUE PROBLEMS
DOI:
https://doi.org/10.29121/granthaalayah.v6.i1.2018.1591Keywords:
BVP, MATLAB, MAPLE, Finite Difference Method, Shooting Method, RK45, RK4, Secant Method, Newton’s MethodAbstract [English]
The paper investigates the efficacy of non-linear two point boundary value problems via shooting and finite difference methods. It was observed that the shooting method provides better result as when compared to the finite difference methods with dirichlet boundary conditions. It was observed that the accuracy of the shooting method is dependent upon the integrator adopted.
Downloads
References
Williams H Press, Brian P Flannery, Saul A Tuekolsky and Williams T Vetterling. (1986). Numerical Recipes. “THE ART OF SCIENTIFIC COMPUTING” Cambridge University Press, New York.
John C Butcher. (2003). “THE NUMERICAL ANALYSIS OF ORDINARY DIFFERENTIAL EQUATIONS”. John Wiley & Sons, UK.
John C Butcher. (1987). “THE NUMERICAL ANALYSIS OF ORDINARY DIFFERENTIAL EQUATIONS”. Runge-Kutta and general linear methods. . John Wiley & Sons, UK.
Mahinder K Jain, satteluri R Iyengar and Rajendra Kumar Jain. (2010). “NUMERICAL METHODS FOR SCIENTIFIC AND ENGINEERING COMPUTATION”. 5th edition. New Age International Publishers, Ne Delhi, India.
Arieh Lserles. (1996). “A FIRST COURSE IN THE NUMERICAL ANALYSIS OF DIFFERENTIAL EQUATIONS”, Cambridge University Press.
James Murray Watt. (1976). “MODERN NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS”, clarendon press.
Runge C. (1895). “EXPLICIT 2ND ORDER RUNGE-KUTTA METHOD” Martin Luther University, Halle-Wittenberg, Halle.
Henrici Peter. (1962). “DISCRETE VARIABLE METHODS IN ODES”, New York John Wiley & Sons.
Leonhard Euler. (1913). “INSTITUTIONAL CALCULI INTEGRALS” primum omnia series prims.
Hubert Harrer, A schuler and E Amelunxen. (1990). “COMPARISON OF DIFFERENT NUMERICAL INTEGRATIONS FOR SIMULATING CELLULOSE NEURAL NETWORKS”. In: proceeding of the IEEE International Workshop on cellular neural networks and their Applications, Budapest, p. 151-159.
Downloads
Published
How to Cite
Issue
Section
License
With the licence CC-BY, authors retain the copyright, allowing anyone to download, reuse, re-print, modify, distribute, and/or copy their contribution. The work must be properly attributed to its author.
It is not necessary to ask for further permission from the author or journal board.
This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge.