Estimating the Error of Field Variable for Numerical Approximation Techniques Using Matlab
[Nitin Sawarkar,Bhushan Mahajan,Manoj Baseshankar,Dnyaneshwar Kawadkar] Volume 1: Issue 1, Dec 2013
Abstract:-The various scientific laws, principles are used to develop mathematical models. Often the differential equations are used to describe the system. But, formulating the differential equations for most problems is difficult and hence obtaining the solutions by exact methods of analysis is a formidable task. The present research discusses the issue of the finding the field variable deviation for quadratic area of one dimensional continuum. The analysis provides the percentage error in the field variable for the selected trial functions. Approximate method is useful, if it is integrated with computer for the problem involving a number of complexities without making drastic assumption which otherwise complicated to attempt by classical methods. A genuine necessity for obtaining precise solution for the different numerical approximation methods is overcome by developing in-house computer program. Graphically results can be displayed to know the effect of considered weights and the constants assumed.
Keywords:-Numerical methods, Field variable, MATLAB, Mathematical modeling.
REFERENCES Day, J.T., and Collins, G.W.,II, "On the Numerical Solution of Boundary Value Problems for Linear Ordinary Differential Equations", (1964), Comm. A.C.M. 7, pp 22-23.  B. Cockburn, G.E.Karniadakis, and Chi-Wang Shu(2000). Discontinuous Galerkin Method: Theory, Computation and applications. Springer-Verlag, Berlin.
 An Introduction to Programming and Numerical Methods in MATLAB - S.R. Otto & J.P. Denier. Springer-Verlag, Berlin.
 Finlayson, B. A. (1972).The Method of Weighted Residuals and Variational Principles, Academic Press, New York,.
 Marquardt, D.W., "An Algorithm for Least-Squares Estimation of Nonlinear Parameters", (1963), J. Soc. Ind. Appl. Math., Vol.11, No. 2, pp.431-441
J.Petrolito(1998). Approximate solutions of differential equations using Galerkin’s method and weighted residuals, Australia, , pp.14-25.
 Mikhlin, S. G. (1963). Variational Methods in Mathematical Physics, Pergamon Press, New York,.
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