David A. Pope
Abstract
A formula for numerical integration is prepared, which involves an exponential term. This formula is compared to two standard integration methods, and it is shown that for a large class of differential equations, the exponential formula has superior stability properties for large step sizes. Thus this formula may be used with a large step size to decrease the total computing time for a solution significantly, particularly in those engineering problems where high accuracy is not needed.
- 1 BROCK, P., AND MURRAY, F .J . The use of exponential sums in step by step integration. Math. Tables Aids Comp. 6 (1952), 63-77, 138-150.Google Scholar
Cross Ref
- 2 BLANCH, G. On the numerical solution of equations involving differential operators with constant coefficients. Math. Tables Aids Comp. 6 (1952), 219-223.Google ScholarCross Ref
- 3 CODDINGTON, E., AND LEVINSON, N. Theory of Ordinary Differential Equations. McGraw-Hill, New York (1955).Google Scholar
- 4 DAVIS, H. T. Introduction to Nonlinear Differential and Integral Equations. Dover Publications, New York (1962).Google Scholar
- 5 DENNIS, S. C. R. The numerical integration of ordinary differential equations possessing exponential type solutions. Proc. Cambridge Philos. Soc. 56 (1960), 240-246.Google ScholarCross Ref
- 6 HENRICI, P. Discrete Variable Methods in Ordinary Differential Equations. Wiley, New York (1962).Google Scholar
- 7 MILNE, W. E. Numerical Solution of Differential Equations. Wiley, New York (1953).Google Scholar
Recommendations
Numerical integration of ordinary differential equations with rapidly oscillatory factors
We present a methodology for numerically integrating ordinary differential equations containing rapidly oscillatory terms. This challenge is distinct from that for differential equations which have rapidly oscillatory solutions: here the differential ...
An asymptotic numerical method for singularly perturbed third-order ordinary differential equations with a weak interior layer
A class of singularly perturbed two point boundary value problems (BVPs) of convection-diffusion type for third-order ordinary differential equations (ODEs) with a small positive parameter (ε) multi-plying the highest derivative and a discontinuous ...
New numerical method for ordinary differential equations: Newton polynomial
AbstractThe Adams–Bashforth have been recognized to be a very efficient numerical method to solve linear and nonlinear differential equations, including those with non-integer orders. This method is based on the well-known Lagrange ...
Highlights- New numerical scheme based on Newton polynomial.
- New numerical scheme for ...
Comments