By Ronald E. Mickens
This quantity presents a concise creation to the method of nonstandard finite distinction (NSFD) schemes building and exhibits how they are often utilized to the numerical integration of differential equations happening within the common, biomedical, and engineering sciences. those equipment had their genesis within the paintings of Mickens within the 1990's and at the moment are starting to be greatly studied and utilized by way of different researchers. the significance of the booklet derives from its transparent and direct clarification of NSFD within the introductory bankruptcy in addition to a large dialogue of the long run instructions had to boost the subject.
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Extra resources for Advances in the Applications of Nonstandard Finite Difference Schemes
F. Abo-Shanab, N. Sepehri a n d C. Q. Wu Time (s) Fig. 2. 0001s. Simulation Studies of Robotic Svstems 23 Time (s) 0 1 2 3 4 5 6 7 Time (s) Fig. 3. Spurious solutions obtained by RK4 method (case study I). 8 R. F. Abo-Shanab, N . Sepehri and C. Q. 09 L 3 c 4or-- 30 4 Time (s) Fig. 4. -- I 5 6 7 , I I Nonconvergent numerical results obtained by RK4 method. 8 -1 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 25 Step size, p (s) Fig. 5. Relation between effective step-size, 9,and the maximum eigenvalue of the discrete system obtained by nonstandard scheme I (case study I).
41 42 R. Abo-Shanab, N . Sepehri and C. Q. Wu Time (s) Fig. 19. 001s). (o, using nonstandard scheme I1 (step--size Simulation Studies of Robotic Systems 43 Time (s) 0 1 2 3 4 5 6 7 8 9 10 Time (s) Fig. 20. Comparison between simulation results of tracking errors using small and large values for the step-size h (scheme 11). 44 R. F. Abo-Shanab, N . Sepehri and C. Q. Wu Time (s) Fig. 21. 001s and h = 10s). 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.
Q. 09 L 3 c 4or-- 30 4 Time (s) Fig. 4. -- I 5 6 7 , I I Nonconvergent numerical results obtained by RK4 method. 8 -1 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 25 Step size, p (s) Fig. 5. Relation between effective step-size, 9,and the maximum eigenvalue of the discrete system obtained by nonstandard scheme I (case study I). R. F. Abo-Shanab, N . Sepehri and C. Q. Wu 26 Time (s) 25 2c 15 0 -5 -1c -15 1 2 3 4 Time (s) 5 6 7 8 Fig. 6. Simulation results using nonstandard scheme I with effective step-sizes less than the critical step-size.
Advances in the Applications of Nonstandard Finite Difference Schemes by Ronald E. Mickens