On Implicit Taylor Series Methods for Sti ODEs
نویسندگان
چکیده
Several versions of implicit Taylor series methods (ITSM) are presented and evaluated. Criteria for the approximate solution of ODEs via ITSM are given. Some ideas, motivations, and remarks on the inclusion of the solution of stii ODEs are outlined.
منابع مشابه
Stability of implicit - explicit linear multistep methods
In many applications, large systems of ordinary di erential equations (ODEs) have to be solved numerically that have both sti and nonsti parts. A popular approach in such cases is to integrate the sti parts implicitly and the nonsti parts explicitly. In this paper we study a class of implicit-explicit (IMEX) linear multistep methods intended for such applications. The paper focuses on the linea...
متن کاملEecient Implementation of Fully Implicit Methods for Atmospheric Chemical Kinetics Eecient Implementation of Fully Implicit Methods
Implicit integrators are very useful in e ciently solving sti systems of ODEs arising from atmospheric chemistry kinetics, provided that they are modi ed to take full advantage of the structure of the problem. A systematic way of treating sparsity for reducing the linear algebra cost is presented. 3 E cient implementation of fully implicit methods 4
متن کاملComputing Validated Solutions of Implicit Differential Equations
Ordinary differential equations (ODEs), including high-order implicit equations, describe important problems in mechanical and chemical engineering. However, the use of selfvalidated methods providing rigorous enclosures of the solution has mostly been limited to explicit and weakly nonlinear problems, and no general-purpose algorithm for the validated integration of general ODE initial value p...
متن کاملThe Effects of Systemic-Theoretical Instruction on Developing Iranian EFL Learners’ Explicit and Implicit Knowledge of Tense-Aspect System
This study aimed to investigate the effects of Systemic Theoretical Instruction (STI), grounded in Socio-cultural Theory and proposed by Gal’perin, on developing Iranian EFL learners’ knowledge of English tense-aspect system. To this end, two low-intermediate classes, including 24 and 21 language learners aged between 12-19, were taught the distinction between simple past and present perfect te...
متن کاملATOMFT: Solving ODES and DAEs Using Taylor Series
Taylor series methods compute a solution to an initial value problem in ordinary differential equations by expanding each component of the solution in a long Taylor series. The series terms are generated recursively using the techniques of automatic differentiation. The ATOMFT system includes a translator to transform statements of the system of ODES into a FORTRAN 77 object program that is com...
متن کامل