## Functions in use for solving ordinary differential equations in Mathcad

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 – 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.