Numerical Methods for Differential Equations: A Computational Approach

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CRC Press, 21 de fev de 1996 - 384 páginas
With emphasis on modern techniques, Numerical Methods for Differential Equations: A Computational Approach covers the development and application of methods for the numerical solution of ordinary differential equations. Some of the methods are extended to cover partial differential equations. All techniques covered in the text are on a program disk included with the book, and are written in Fortran 90. These programs are ideal for students, researchers, and practitioners because they allow for straightforward application of the numerical methods described in the text. The code is easily modified to solve new systems of equations.
Numerical Methods for Differential Equations: A Computational Approach also contains a reliable and inexpensive global error code for those interested in global error estimation. This is a valuable text for students, who will find the derivations of the numerical methods extremely helpful and the programs themselves easy to use. It is also an excellent reference and source of software for researchers and practitioners who need computer solutions to differential equations.
 

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Conteúdo

Differential equations
1
Multistep formulae from quadrature
9
Second order equations
14
First ideas and singlestep methods
15
Error considerations
31
RungeKutta methods
47
Stepsize control
71
Dense output
97
Methods for Stiff systems
189
Variable coefficient multistep methods
211
Global error estimation
231
A Programs for single step methods
291
B Multistep programs
305
Programs for Stiff systems
327
Global embedding programs
339
E A RungeKutta Nyström program
355

Stability and stiffness
117
Multistep methods
135
Stability of multistep methods
167

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Página 361 - Dormand. JR, Duckers, RR and Prince, PJ (1984): Global error estimation with Runge-Kutta methods. IMA J.
Página 361 - PJ (1978): New Runge-Kutta-Nystrom algorithms for simulation in dynamical astronomy. Celestial Mechanics 18, 223-232.
Página 361 - Prince, PJ and Seward. WL (1989): A Runge-Kutta-Nystrom code. ACM Trans. Math.

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