By Ronald E. Mickens
This quantity offers a concise creation to the technique of nonstandard finite distinction (NSFD) schemes building and indicates how they are often utilized to the numerical integration of differential equations taking place within the usual, biomedical, and engineering sciences. those tools had their genesis within the paintings of Mickens within the 1990's and are actually commencing to be extensively studied and utilized through different researchers. the significance of the ebook derives from its transparent and direct rationalization of NSFD within the introductory bankruptcy in addition to a wide dialogue of the longer term instructions had to enhance the subject.
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Extra resources for Advances in the Applications of Nonstandard Finite Difference Schemes
Mickens, Applications of Nonstandard Finite Difference Schemes, (World Scientific, Singapore, 2000). R. Anguelov and J. Lubuma, Contributions to the mathematics of the nonstandard finite difference method and applications, Journal of Numerical Methods for Partial Differential Equations 17 (2001), 518-543. R. E. Mickens, Discretizations of nonlinear differential equations using explicit nonstandard methods, Journal of Computational and Applied Mathematics 110 (1999), 181-185. P. Sekhavat, N. Sepehri and Q.
F,(x~)}~) pertaining to fixed (equilibrium) point, R , of the original differential system. The use of function (19) allows the value of h to be selected much larger than one normally choose, because it is the effective step-size p that determines the stability and not the actual step-size h. An acceptable value for p is the one for which the maximum eigenvalue of the Jacobian matrix R is less than 1. , the fixed point of the discrete derivatives has the same stability properties as those of the critical (fixed) point of the original system.
5 . Conclusions In this chapter, two nonstandard finite difference (NSFD) schemes were employed to, for the first time, study numerical solutions of the equations of motion of a typical robot manipulator. The simulation results were also compared with the ones obtained using the conventional fourth-order Runge-Kutta (RK4) algorithm. It was shown that by using the proper choice of the scheme and the nonlocal substitutions, (i) the possibility of having spurious solutions obtained by the RK4 method is eliminated, (ii) stability properties of the original system are preserved, and (iii) simulation results are numerically stable given any selected value of the step-sizes.
Advances in the Applications of Nonstandard Finite Difference Schemes by Ronald E. Mickens
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