![]() ![]() ![]() In the example above, h denotes the step size and the coefficients are determined by the method used. An example of these would be the following: The Adams and Gear methods are forms of linear multistep methods. These algorithms are the Adams method and the Gear method. Mathematica uses two main algorithms in order to determine the solution to a differential equation. Note: Remember to type "Shift"+"Enter" to input the function X t = &ExponentialE − t, y t = − &ExponentialE − t + &ExponentialE −1įor detailed information on the dsolve command, see dsolve/details. Coupled non-linear differential equations. Solve the system of ODEs subject to the initial conditions ics. X t = c_2 &ExponentialE − t, y t = − c_2 &ExponentialE − t + c_1 If the unknowns are not specified, all differentiated indeterminate functions in the system are treated as the unknowns of the problem. In order to that, I have tried to solve the system simbologically with sympy. Sys_ode ≔ &DifferentialD &DifferentialD t y t = x t, &DifferentialD &DifferentialD t x t = − x t This equations defines a kinetick model and I need to solve them to get the Y(t) function to fit my data and find k3 and k4 values. Sys_ode ≔ &DifferentialD &DifferentialD t y t = x t, &DifferentialD &DifferentialD t x t = − x t Odetest series_sol, ode, ics, series This does a machine precision computation of a numerical integral: In 1. But by setting the option WorkingPrecision ->n you can tell it to use arbitrary precision numbers with n digit precision. Series_sol ≔ y x = 1 + 3 2 x 2 + 1 4 x 4 + O x 6 In doing numerical operations like NDSolve and NMinimize, the Wolfram Language by default uses machine numbers. Series_sol ≔ dsolve ode, ics, y x, series Test whether the ODE solution satisfies the ODE and the initial conditions (see odetest ).įind a series solution for the same problem. Sol ≔ dsolve ode, ics, y x, method = laplace Y x = 3 &ExponentialE 2 x 4 + 3 &ExponentialE − 2 x 4 − 1 2Ĭompute the solution using the Laplace transform method. Solve ode subject to the initial conditions ics. Y x = &ExponentialE 2 x c_2 + &ExponentialE − 2 x c_1 − 1 2 ![]() Ode ≔ &DifferentialD 2 &DifferentialD x 2 y x = 2 y x + 1 Ode ≔ &DifferentialD 2 &DifferentialD x 2 y x = 2 y x + 1 To define a derivative, use the diff command or one of the notations explained in Derivative Notation. Mathematica is a powerful package that is capable of solving coupled differential equations symbolically. For more information, see dsolve and worksheet/interactive/dsolve. Using the assistant, you can compute numeric and exact solutions and plot the solutions. The ODE Analyzer Assistant is a point-and-click interface to the ODE solver routines. Computing numerical (see dsolve/numeric ) or series solutions (see dsolve/series ) for ODEs or systems of ODEs. Computing solutions using integral transforms (Laplace and Fourier). Computing formal solution for a linear ODE with polynomial coefficients. Computing formal power series solutions for a linear ODE with polynomial coefficients. Solving ODEs or a system of them with given initial conditions (boundary value problems). Computing closed form solutions for a single ODE (see dsolve/ODE ) or a system of ODEs, possibly including anti-commutative variables (see dsolve/system ). (See the Examples section.)Īs a general ODE solver, dsolve handles different types of ODE problems. (optional) depends on the type of ODE problem and method used, for example, series or method=laplace. , where are constants with respect to the independent variable Initial conditions of the form y(a)=b, D(y)(c)=d. This paper proposes the existence and uniqueness of a solution for a coupled system that has fractional differential equations through Erdlyi-Kober and. Ordinary differential equation, or a set or list of ODEsĪny indeterminate function of one variable, or a set or list of them, representing the unknowns of the ODE problem Solve ordinary differential equations (ODEs) ![]()
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