ZigangPan/DifferentialEquationSolver

ZigangPan`DifferentialEquationSolver`

flow

[f,xc,

t

0

]

calculates the solution to the system of ordinary differential equation

xc'[t]=f[xc1[t],xc2[t],...,xcn[t]]

;

xc[t0]

=xc0; where

f

is the vector field (a pure function),

xc

is the state vector,and xc0 is the initial condition at time

t0

. The return of the function is a function sol[xc0_,t_] that satisfies the desired differential equation and the initial condition. (This function tries to solve the differential equation for all initial conditions.)

Examples

(1)

Basic Examples

(1)

In[1]:=

f[x1_,x2_]:={-x1,x1^2-x2};xc={x1,x2};t0=0;

In[2]:=

sol=

flow

[f,xc,t0]

Out[2]=

Function{x10,x20,Private`t$9408},

x10

Private`t$9408



,

-

2

x10

+

Private`t$9408



2

x10

+

Private`t$9408



x20

2Private`t$9408





In[3]:=

Plot[sol[2,1,t],{t,0,10},PlotRangeAll]

Out[3]=

SeeAlso

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