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The Vector Field: Multipliers and Combinations

  • Mike R. Jeffrey
Chapter

Abstract

Consider a set of ordinary differential equations
$$\displaystyle{\frac{dx_{1}} {dt} = f_{1}(x_{1},x_{2},\ldots,x_{n})\;,\quad \frac{dx_{2}} {dt} = f_{2}(x_{1},x_{2},\ldots,x_{n})\;,\quad \ldots \quad etc.}$$
or more concisely collecting the state variables xi into an n-dimensional vector x = (x1, x2, , xn), and the functions fi into a vector f = (f1, f2, , fn), with the derivative with respect to time t denoted by a dot.

References

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    A. F. Filippov. Differential Equations with Discontinuous Righthand Sides. Kluwer Academic Publ. Dortrecht, 1988 (Russian 1985).Google Scholar
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    T. I. Seidman. Existence of generalized solutions for ordinary differential equations in Banach spaces. Int. J. Evolution Equations, 1:107–119, 2005.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Mike R. Jeffrey
    • 1
  1. 1.Department of Engineering MathematicsUniversity of BristolBristolUK

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