By Robert Grossman
ISBN-10: 0898712394
ISBN-13: 9780898712391
Here's a monograph that describes present study efforts within the program of symbolic computation to numerous parts, together with dynamical structures, differential geometry, Lie algebra's, numerical research, fluid dynamics, perturbation concept, regulate idea, and mechanics. The chapters, which illustrate how symbolic computations can be utilized to review quite a few mathematical buildings, are outgrowths of the invited talks that have been awarded on the NASA-Ames Workshop at the Use of Symbolic tips on how to clear up Algebraic and Geometric difficulties coming up in Engineering. greater than a hundred humans participated within the two-day convention, which came about in January 1987 on the NASA-Ames study heart in Moffett box, California.
The box of symbolic computation is turning into more and more vital in technology, engineering, and arithmetic. the provision of robust machine algebra structures on workstations has made symbolic computation an incredible instrument for plenty of researchers.
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Additional resources for Symbolic Computation: Applications to Scientific Computing (Frontiers in Applied Mathematics)
Sample text
The method is applied to the system derivative, producing an integrator which, given a data structure that contains a state and a step-size, integrates for one step. In order to admit integrators with adaptive step-size control, integrator is structured to return not only the next state, but also a predicted next step-size, wrapped up in a data structure constructed by make-state-and-step. The result produced by the integration driver is a procedure next which, given an initial state and an initial step-size, evolves the sequence of states, passing each state to an output procedure (which, for example, produces graphical output).
13 The meaning of the final four components of the state is that VC[^*L], for example, is the component in the direction vc of the variation vector S%L14 See Abraham and Shaw [2] for fewer details. 1))))))) 3)) 4)) 5)) 6))) Figure 11. This is the augmented system derivative generator compiled to evolve variational states for the driven van der Pol oscillator. Reprinted with permission from Communications of the ACM, Vol. 32, p. 559. © 1989 by the Association for Computing Machinery, Inc. DYNAMICIST'S WORKBENCH 47 where DXS and DpS are the matrices of partial derivatives of S with respect to x and p.
The top graph shows the power dissipated in resistor rl. The vertical scale here is [0,5] watts. DYNAMICIST'S WORKBENCH 23 lation is a first-order system of the form: The resulting algebraic expressions for the components of the system derivative, f, are compiled to form a system-derivative generator procedure. The generator takes as arguments numerical values for the system parameters and produces a system-derivative procedure, which takes a system state vector as argument and produces a differential state (a vector that when multiplied by an increment of time is an increment of state).
Symbolic Computation: Applications to Scientific Computing (Frontiers in Applied Mathematics) by Robert Grossman
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