Functions in use for solving ordinary differential equations in Mathcad
In order to solve ordinary differential equations and sets of ordinary differential equations Mathcad offers a number of functions:
- odesolve(x,b,step) is used for solving the ordinary differential equation, assigned either in form of Cauchy problem or in form of the boundary-value problem. Initial conditions and the differential equation are to be settled in case given. Function parameters: х –variable for integration; b – finite value of solution interval; step – stride parameter of the numerical procedure (not compulsory).
- rkfixed(u,a,b,N,D) realizes in Mathcad the numerical procedure for Cauchy problem using Runge-Kutta method with the fixed stride (step). Takes advantage over odesolve(x,b,step) in the following: can be used in programme packages and lets recount the results immediately in case of any parameter change. Function parameters: u-initial conditions vector; a и b – boundary values of problem solution interval; N – number of intervals fragment [a,b] is divided into; D(x,y) –vector-function, containing the right segments of the first derivatives, written down in a character way.
- Rkadapt(u, a,b, N, D) – returns matrix in Mathcad, which contains the value table of Cauchy problem solutions at the interval from a to b for the equation or the set of differential equations, calculated with Runge-Kutta method with the variable stride (step) and initial conditions in vector u, D(x,y) –vector-function, containing the right segments of the first derivatives, written down in a character way, n – number of strides (steps).
- Function Rkadapt() due to the automatic selection of strides normally gives a more accurate result in comparison with other Mathcad functions.