Differential eguations： modify the program

Differential eguations

dy1/dt=-a*y1+y2*y3

dy2/dt=-b(y2-y3)

dy3/dt=-a*y2+ y3-3*y2*y3

a=4 b=8 c=30

y1(0)=0

y2(0)=0

y3(0)=10-10 =0.0000000001

MATLAB ODE45_main：

tspan=[0,100];

y0=[0; 0;10^(-10)];

[t,y]=ode45('ODE45_fun',tspan,y0);

data=[t,y];

save ODE45_data.txt data –ascii

plot3(y(:,1), y(:,2), y(:,3))

grid on

MATLAB ODE45_fun：

function dy=ODE45_fun(t,y)

a=4; b=18; c=30;

dy(1)=-a*y(1)+y(2)*y(3);

dy(2)=-b*(y(2)-2*y(3));

dy(3)=c*y(2)-y(3)-3*y(2)*y(1);

dy=[dy(1);dy(2);dy(3)];

The program can work without any error. If the formula for y4:

y4=-3*y2*y3-4*y1*y3+8*y1*y3

How can I modify the program? And the curve of y4 ?

Answer 1

[Torsten]

tspan=[0,100];
y0=[0; 0;10^(-10);0];
M=[1 0 0 0
   0 1 0 0
   0 0 1 0
   0 0 0 0];
options=odeset('Mass',M);
[t,y]=ode45(@ODE45_fun,tspan,y0,options);

function dy=ODE45_fun(t,y)
a=4; b=18; c=30;
dy(1)=-a*y(1)+y(2)*y(3);
dy(2)=-b*(y(2)-2*y(3));
dy(3)=c*y(2)-y(3)-3*y(2)*y(1);
dy(4)=y(4)-(-3*y(2)*y(3)-4*y(1)*y(3)+8*y(1)*y(3));
dy=[dy(1);dy(2);dy(3);dy(4)];

Best wishes

Torsten.

[jixie zhuangbei]

MATLAB 7

In funfun\private\odemassexplicit>ExplicitSolverHandleMass1 at 38 In ode45 at 328 In ODE45_main at 8 Warning: Matrix is singular to working precision. > In funfun\private\odemassexplicit>ExplicitSolverHandleMass1 at 38 In ode45 at 337 In ODE45_main at 8 Warning: Matrix is singular to working precision. > In funfun\private\odemassexplicit>ExplicitSolverHandleMass1 at 38 In ode45 at 324 In ODE45_main at 8 Warning: Matrix is singular to working precision. > In funfun\private\odemassexplicit>ExplicitSolverHandleMass1 at 38 In ode45 at 325 In ODE45_main at 8 Warning: Matrix is singular to working precision. > In funfun\private\odemassexplicit>ExplicitSolverHandleMass1 at 38 In ode45 at 326 In ODE45_main at 8 Warning: Matrix is singular to working precision. > In funfun\private\odemassexplicit>ExplicitSolverHandleMass1 at 38 In ode45 at 327 In ODE45_main at 8 Warning: Matrix is singular to working precision. > In funfun\private\odemassexplicit>ExplicitSolverHandleMass1 at 38 In ode45 at 328 In ODE45_main at 8 Warning: Matrix is singular to working precision. > In funfun\private\odemassexplicit>ExplicitSolverHandleMass1 at 38 In ode45 at 337 In ODE45_main at 8 Warning: Matrix is singular to working precision. > In funfun\private\odemassexplicit>ExplicitSolverHandleMass1 at 38 In ode45 at 324 In ODE45_main at 8 Warning: Matrix is singular to working precision. > In funfun\private\odemassexplicit>ExplicitSolverHandleMass1 at 38 In ode45 at 325 In ODE45_main at 8 Warning: Matrix is singular to working precision. > In funfun\private\odemassexplicit>ExplicitSolverHandleMass1 at 38 In ode45 at 326 In ODE45_main at 8 Warning: Matrix is singular to working precision. > In funfun\private\odemassexplicit>ExplicitSolverHandleMass1 at 38 In ode45 at 327 In ODE45_main at 8 Warning: Matrix is singular to working precision. > In funfun\private\odemassexplicit>ExplicitSolverHandleMass1 at 38 In ode45 at 328 In ODE45_main at 8 Warning: Matrix is singular to working precision. > In funfun\private\odemassexplicit>ExplicitSolverHandleMass1 at 38 In ode45 at 337 In ODE45_main at 8 Warning: Matrix is singular to working precision. > In funfun\private\odemassexplicit>ExplicitSolverHandleMass1 at 38 In ode45 at 324 In ODE45_main at 8 .....................................

[Torsten]

I see now that ODE45 can not handle a singular mass matrix.

Use ODE15S instead.

Best wishes

Torsten.