By Ronald E. Mickens

ISBN-10: 9812564047

ISBN-13: 9789812564047

ISBN-10: 9812703314

ISBN-13: 9789812703316

This quantity offers a concise creation to the technique of nonstandard finite distinction (NSFD) schemes development and exhibits how they are often utilized to the numerical integration of differential equations happening within the traditional, biomedical, and engineering sciences. those equipment had their genesis within the paintings of Mickens within the 1990's and at the moment are commencing to be broadly studied and utilized via different researchers. the significance of the e-book derives from its transparent and direct rationalization of NSFD within the introductory bankruptcy in addition to a extensive dialogue of the long run instructions had to improve the subject.

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**Extra resources for Advances in the Applications of Nonstandard Finite Difference Schemes**

**Sample text**

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. Wu, Calculation of Lyapunov exponent using nonstandard finite difference discretizations scheme: a case study, Journal of Differential Equations and Applications 10 (2004), 369-378.

S i m u l a t i o n S t u d i e s of Robotic S y s t e m s 15 where D = M-'(q). The following states are now used: Zl = x 2 = q1 x2 =q1 x 3 = x4 = 92 x 4 = 42 In a general form, one can write i i = l , 3 , 5, . . ,2 4 4 = {D[T- H(x) - G ( x ) ] } ~ i = 2 , 4 , 6 , . . , 2 n (12) where n is the number of the manipulator's degrees of freedom, and {. . }i represents the ith element of the vector {. . }. 3. Constructing the Discrete Derivatives Two nonstandard finite difference schemes are used to construct the discrete derivatives of the above system.

The effective step size is shown in Figure 19. Figure 20 shows Simulation Studies of Robotic Systems 33 the simulation of the tracking errors given the step-size h = 10s. As is seen, the scheme still indicates correct indication regarding the stability of the fixed point even with this large step-size. 025s when the actual step-size was changed to 10s. 0 1 2 3 4 5 6 7 8 9 10 6 7 8 9 10 Time (s) 0 1 2 3 4 5 Time (s) Fig. 10. Desired joint trajectories (case study 11). R. F. Abo-Shanab, N . Sepehri a n d C.

### Advances in the Applications of Nonstandard Finite Difference Schemes by Ronald E. Mickens

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