Abstract
This paper presents a method of numerical integration for Stieltjes integration, a construction of a High Accuracy Digital Differential Analyzer based on the method and a few experimental results which show a high computation accuracy and flexibility of the HADDA.
A formula of numerical Stieltjes integration is obtained from Adams method of numerical integration and a formula of numerical differentiation which comes from differentiation of the Newton backward interpolation polynomial. A digital integrator based on this formula is designed and constructed by a minicomputer. A few differential equations are solved by the constructed HADDA and the accuracy of these solutions are investigated.
The experimental results show that (1) the computation error of the HADDA is of order of Δt2 while that of the existing DDA's is of order of Δt, where Δt is the incremental size of a independent variable t, (2) the computation speed of the HADDA is about 1/2 of that of the DDA's (3) furthermore, the extension of highly accurate integration from time integral to a more general Stieltjes integration makes the flexibility of the HADDA much higher. For example, it becomes possible to solve nonlinear differential equations much more accurately.
