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Among ordinary differential equations, linear differential equations play a prominent role for several reasons. Most elementary and special functions that are encountered in physics and applied mathematics are solutions of linear differential equations (see Holonomic function ).
Ordinary differential equations occur in many scientific disciplines, including physics, chemistry, biology, and economics. [1] In addition, some methods in numerical partial differential equations convert the partial differential equation into an ordinary differential equation, which must then be solved.
Floquet theory is a branch of the theory of ordinary differential equations relating to the class of solutions to periodic ... (PDF), Annales ... 12: 47–88, doi: 10 ...
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. [1] In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two.
Differential equations are an important area of mathematical analysis with many applications in science and engineering. Analysis is the branch of mathematics dealing with continuous functions , limits , and related theories, such as differentiation , integration , measure , infinite sequences , series , and analytic functions .
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118: 454–7. (In that article Lindelöf discusses a generalization of an earlier approach by Picard.) Teschl, Gerald (2012). "2.2. The basic existence and uniqueness result" (PDF). Ordinary Differential Equations and Dynamical Systems. Graduate Studies in Mathematics. Providence, Rhode Island: American Mathematical Society. p. 38. eISSN 2376-9203.
The backward differentiation formula (BDF) is a family of implicit methods for the numerical integration of ordinary differential equations.They are linear multistep methods that, for a given function and time, approximate the derivative of that function using information from already computed time points, thereby increasing the accuracy of the approximation.