论文信息 - Block Method for Generalised Multistep Adams and Backward Differentiation Formulae In Solving First Order ODEs

Block Method for Generalised Multistep Adams and Backward Differentiation Formulae In Solving First Order ODEs

The performance of the Block Generalised Multistep Adams and Backward Differentiation Formulae (BGMBDF) as compared with Generalised Multistep Adams and Backward Differentiation Formulae (GMBDF) is presented. These methods are used to solve initial value problems (IVPs) for stiff and nonstiff systems of ordinary differential equations (ODEs). The results obtained show that the BGMBDF reduces the total number of steps in computation. Keywords: Block; backward differentiation formulae; steps. Closure matroid.

[1] T. E. Hull,et al. Comparing Numerical Methods for Ordinary Differential Equations , 1972 .

[2] Simeon Ola Fatunla,et al. Block methods for second order odes , 1991, Int. J. Comput. Math..

[3] D. Arnold,et al. Computer Solution of Ordinary Differential Equations. , 1981 .

[4] Moody T. Chu,et al. Parallel solution of ODE's by multi-block methods , 1987 .

[5] John C. Butcher,et al. A Modified Multistep Method for the Numerical Integration of Ordinary Differential Equations , 1965, JACM.

[6] Louis G. Birta,et al. Parallel Block Predictor–Corrector Methods for Ode's , 1987, IEEE Transactions on Computers.

[7] M. Suleiman,et al. Developing parallel block method for solving higher order ODEs directly , 2002 .

[8] D. A. Voss,et al. Block predictor-corrector schemes for the parallel solution of ODEs , 1997 .

[9] H. A. Watts,et al. Block Implicit One-Step Methods* , 1969 .

[10] J. Douglas Faires,et al. Numerical Analysis , 1981 .

[11] W. Miranker. A Survey of Parallelism in Numerical Analysis , 1971 .

[12] Jürg Nievergelt,et al. Parallel methods for integrating ordinary differential equations , 1964, CACM.

[13] J. Miller. Numerical Analysis , 1966, Nature.

[14] Robert D. Russell,et al. A COMPARISON OF COLLOCATION AND FINITE DIFFERENCES FOR TWO-POINT BOUNDARY VALUE PROBLEMS* , 1977 .