2 edition of **Solving ordinary differential equations with discontinuities** found in the catalog.

Solving ordinary differential equations with discontinuities

C. William Gear

- 203 Want to read
- 17 Currently reading

Published
**1981**
by Dept. of Computer Science, University of Illinois at Urbana-Champaign in Urbana, Ill
.

Written in English

- Differential equations -- Numerical solutions -- Data processing.,
- Discontinuous functions.

**Edition Notes**

Statement | by C.W. Gear and O. Østerby. |

Series | Rept. / Department of Computer Science, University of Illinois at Urbana-Champaign ;, no. UIUCDCS-R-81-1064, Report (University of Illinois at Urbana Champaign. Dept. of Computer Science) ;, no. UIUCDCS-R-81-1064. |

Contributions | Østerby, O. |

Classifications | |
---|---|

LC Classifications | QA76 .I4 no. 1064, QA372 .I4 no. 1064 |

The Physical Object | |

Pagination | 67 p. : |

Number of Pages | 67 |

ID Numbers | |

Open Library | OL3143495M |

LC Control Number | 82621003 |

Areas of Scientific Consulting Expertise. Numerical Solutions to Ordinary and Partial Differential Equations. Our company has developed algorithms and contributed to a number of publications for solving ordinary and partial differential equations. Learn more. Computer Vision & . We use the reproducing kernel method (RKM) with interpolation for finding approximate solutions of delay differential equations. Interpolation for delay differential equations has not been used by this method till now. The numerical approximation to the exact solution is computed. The comparison of the results with exact ones is made to confirm the validity and by:

Ordinary Differential Equations William A. Adkins, Mark G. Davidson Unlike most texts in differential equations, this textbook gives an early presentation of the Laplace transform, which is then used to motivate and develop many of the remaining differential equation concepts for which it is particularly well suited. Ordinary differential equations are coupled with mixed constrained optimization problems when modeling the thermodynamic equilibrium of a system evolving with time. A particular application arises in the modeling of atmospheric by: 9.

For example, Hairer's benchmarks in his book Solving Ordinary Differential Equations I and II (the second is for stiff problems), along with the benchmarks from the Julia suite, consistently show that high order Runge-Kutta methods are usually the most efficient methods for high accuracy solving of nonstiff ODEs. These. Dynamic models that arise in health physics applications are often expressed in terms of systems of ordinary differential equations. In many cases, such as box models that describe material exchange among reservoirs, the differential equations are linear with constant coefficients, and the analysis can be reduced to the examination of solutions of initial-value problems for such .

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Part of the Progress in Theoretical Computer Science book series (PTCS) Abstract Our aim is to extend the theory of differential fields such that the “classical algorithm” like the Risch structure theorem and the algorithm solving the Risch differential equation can be extended to handle discontinuous : Martin von Mohrenschildt.

@article{osti_, title = {Solving ordinary differential equations with discontinuities}, author = {Gear, C. and Osterby, O.}, abstractNote = {An algorithm is described that can detect and locate some discontinuities and provide information about their size, order and position.

However, the success of the algorithm is strongly dependent. Hussain K, Ismail F and Senu N () Solving directly special fourth-order ordinary differential equations using Runge-Kutta type method, Journal of Computational and Applied Mathematics, C, (), Online publication date: 1-Nov In what follows, we argue that Eq.

(2) can be solved by solving four ordinary differential equations (ODEs), one for each of the functions T, Θ, Φ, and algebra is somewhat tedious, but we are doing what we have done before. That is, we show, one step at a time, that independence of an expression of certain variables forces the expression to be constant.

A Second Order Scheme for Solving Optimization-Constrained Differential Equations with Discontinuities dif ferential equations with discontinuities 3. Introduction to Advanced Numerical Differential Equation Solving in Mathematica Overview The Mathematica function NDSolve is a general numerical differential equation solver.

It can handle a wide range of ordinary differential equations (ODEs) as well as some partial differential equations (PDEs). In a system of ordinary differential equations there can be any number ofFile Size: 6MB. Request PDF | Solving Differential Equations in R | Both Runge-Kutta and linear multistep methods are available to solve initial value problems for ordinary differential equations in the R.

This book deals with methods for solving nonstiff ordinary differential equations. The first chapter describes the historical development of the classical theory, and the second chapter includes a modern treatment of Runge-Kutta and extrapolation methods.

Chapter three begins with the classical theory of multistep methods, and concludes with the theory of general. In mathematics, a stiff equation is a differential equation for which certain numerical methods for solving the equation are numerically unstable, unless the step size is taken to be extremely has proven difficult to formulate a precise definition of stiffness, but the main idea is that the equation includes some terms that can lead to rapid variation in the solution.

Abstract. Both Runge-Kutta and linear multistep methods are available to solve initial value problems for ordinary differential equations in the R packages deSolve and all of these solvers use adaptive step size control, some also control the order of the formula adaptively, or switch between different types of methods, depending on the local Cited by: 7.

Welcome to Differential Equations at 17Calculus. Differential Equations is a vast and incredibly fascinating topic that uses calculus extensively. This page gets you started on Ordinary/Elementary Differential Equations usually covered in a first semester differential equations course.

In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a computer model.A special case is ordinary differential equations (ODEs), which deal with.

Solving Partial Differential Equations. In a partial differential equation (PDE), the function being solved for depends on several variables, and the differential equation can include partial derivatives taken with respect to each of the variables. Partial differential equations are useful for modelling waves, heat flow, fluid dispersion, and other phenomena with spatial behavior that.

There are two main methods for solving fractional differential equations: (1) transformation to an ordinary differential equation, and (2) using the Laplace transform. To transform to an ordinary differential equation, care must be taken because the ordinary chain rule from calculus does not apply to fractional derivatives.

discontinuities that can be expressed in terms of step functions in a natural way. The Dirac delta function and differential equations that use the delta function are also developed here. The Laplace transform works very well as a tool for solving such differential equations.

Sections – are a rather extensive treatment ofFile Size: 4MB. CONTENTS Application Modules vii Preface ix About the Cover viii CHAPTER 1 First-Order Differential Equations 1 Differential Equations and Mathematical Models 1 Integrals as General and Particular Solutions 10 Slope Fields and Solution Curves 19 Separable Equations and Applications 32 Linear First-Order Equations 48 Substitution Methods.

On the Speed of Propagation of Discontinuities. On the Behavior of Integral Curves for a System of Ordinary. On the Number of Limit Cycles for the Equation 4 d Qx constructed contains continuous convergence coordinates corresponding curve defined definition Denote depends derivatives difference differential equations.

"Solving Ordinary Differential Equations with Discontinuities." ACM Trans. Math. Soft. 10 (): 23 – [G91] Gustafsson, K. "Control Theoretic Techniques for Stepsize Selection in Explicit Runge – Kutta Methods.". Numerical methods for systems of first order ordinary differential equations are tested on a variety of initial value problems.

The methods are compared primarily as to how well they can handle relatively routine integration steps under a variety of accuracy requirements, rather than how well they handle difficulties caused by discontinuities, stiffness, roundoff or getting by: ORDINARY DIFFERENTIAL EQUATIONS IV: Laplace Transform Method David Levermore Department of Mathematics University of Maryland 26 April Because the presentation of this material in lecture will diﬀer from that in the book, I felt that notes that closely follow the lecture presentation might be appreciated.

Laplace Transform Method. SpringerSeriesin 8 Computational Mathematics Editorial Board R. Bank R.L. Graham J.

Stoer R. Varga H. Yserentant.Solving Ordinary Differential Equations I: Nonstiff Problems Ernst Hairer, Syvert P. Nørsett, Gerhard Wanner. I bought this book just because I have been using MATLAB's ODE function to simulate my physiological models.

The MATLAB mannual recommend it. Although I found its content very useful for me, it is too much mathematics.Ordinary Differential Equations Using MATLAB.

NEW - The text is now compatible with MATLAB 5. NEW - The text has been extensively exercises at various levels of difficulty have been added to aid a wider diversity of readers in their introduction to MATLAB bility: This item has been replaced by .