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Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as " numerical integration ", although this term can also refer to the computation of integrals .
The few non-linear ODEs that can be solved explicitly are generally solved by transforming the equation into an equivalent linear ODE (see, for example Riccati equation). [5] Some ODEs can be solved explicitly in terms of known functions and integrals. When that is not possible, the equation for computing the Taylor series of the solutions may ...
In mathematics, the annihilator method is a procedure used to find a particular solution to certain types of non-homogeneous ordinary differential equations (ODEs). [1] It is similar to the method of undetermined coefficients, but instead of guessing the particular solution in the method of undetermined coefficients, the particular solution is determined systematically in this technique.
In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations.The idea is to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree) and a number of points in the domain (called collocation points), and to select that solution which satisfies the ...
In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value.
In mathematics, the method of characteristics is a technique for solving partial differential equations. Typically, it applies to first-order equations , though in general characteristic curves can also be found for hyperbolic and parabolic partial differential equation .
In numerical analysis, the Cash–Karp method is a method for solving ordinary differential equations (ODEs). It was proposed by Professor Jeff R. Cash [1] from Imperial College London and Alan H. Karp from IBM Scientific Center. The method is a member of the Runge–Kutta family of ODE solvers. More specifically, it uses six function ...
Linear multistep methods are used for the numerical solution of ordinary differential equations.Conceptually, a numerical method starts from an initial point and then takes a short step forward in time to find the next solution point.