抄録
This paper proposes symbolic-numerical hybrid computing approach for evaluating derivates accurately. The derivatives are necessary (or at least very useful) in the computational solution of nonlinear problems. There are two approaches for evaluating derivatives in conventional scientific computation: analytically obtained by symbolic computing with symbolic algebra packages; or approximated by finite difference in numerical computing. The symbolic computing is surely reasonable in logicality and mathematics but is impossible in practice for large size problems because of asymptotically exponential or exponential computing complexity. On the other hand, the error analysis shows that finite difference approach only can provide limited accuracy of derivatives. Our symbolic-numerical hybrid computing approach establishes a bridge between symbolic computing and numerical computing, and achieves a good balance between computing complexity and accuracy for evaluating derivatives. The results of simulating computing have illustrated that the hybrid computing approach proposed in this paper is valid.
