Numerical Methods for Differential Equations: A Computational Approach
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.
Multistep formulae from quadrature
First ideas and singlestep methods
Stability and stiffness
Global error estimation
Second order equations
Partial differential equations
A Programs for single step methods
B Multistep programs
Programs for Stiff systems
Outras edições - Ver todos
absolute stability accuracy applied approximation Assuming CALL Chapter coefficients compared component compute condition consider constant construction containing continuous Corrector cost defined dense output dependent derivative determined difference differential equations earlier embedded error coefficients error estimate estimate evaluations example explicit expressed extension extra extrapolation Figure FSAL function given gives global error higher implicit important increase initial value integration interpolant interval iteration linear method multistep neqs numerical numerical solution obtained orbit order formula pair parameters polynomial possible predicted Predictor principal PRINT problem properties READ REAL KIND reduced rejected relation RK formula Runge-Kutta satisfy scheme second order shown similar simple solved specified stability stage step step-size steplength SUBROUTINE Substituting Table Taylor series technique third order tolerance true solution truncation error usually variable yields Yn+1
Página 361 - Dormand. JR, Duckers, RR and Prince, PJ (1984): Global error estimation with Runge-Kutta methods. IMA J.