ode_solve ( func, y, t, abs_tol = 1.0e-10, rel_tol = 1.0e-10 ) Types: func Stmt y double[] t double[] abs_tol double[] rel_tol double
double[] (solution at desired points)
dy/dt = f(t,y) , or, in component form, dy(i)/dt = f(i) = f(i,t,y(1),y(2),...,y(neq)) (i = 1,...,neq).This function switches automatically between stiff and nonstiff methods. This means that the user does not have to determine whether the problem is stiff or not, and the solver will automatically choose the appropriate method. It always starts with the nonstiff method.
Xi the the ordinary differential equation will be determined in a similar way like writing it down on a piece of paper. (y; t) -> y': y' = f (y,t) The vector y describes the initial values for y at the point t[0] and the vector t gives the desired values of the independent variable. The optional variable rel_tol is the relative tolerance parameter. Vector abs_tol gives the absolute tolerance parameter. The estimated local error in y[i] will be controlled so as to be less than
error[i] = rel_tol*abs(y[i]) + abs_tol[i]
( 1)>t=interval(0,5,10); Function interval defined ( 2)>y=ode_solve([ (y; t)->y' : y'=2*y*t+t*t*t; ], {-0.5}, t,\rel_tol=1e-14); ( 3)>plot(t,y,\curve,\marker=4); ( 4)>t=interval(0,2*~pi,100); ( 5)>double[] f(double y[]) { return { y[1], -y[0] }; } Function f defined ( 6)>y=ode_solve([ (y; t)->y' : y'=f(y);], {0,1}, t); ( 7)>window(0,\clearAll); ( 8)>plot(y[0,*], y[1,*],\curve); ( 9)>u=replicate(x=interval(-1,1,9),10); ( 10)>velocity_field(-transpose(u), u, x, x); Function arrowHead defined Function velocity_field defined Function error defined
c authors.. c linda r. petzold c applied mathematics division 8331 c sandia national laboratories c livermore, ca 94550 c and c alan c. hindmarsh, c mathematics and statistics division, l-316 c lawrence livermore national laboratory c livermore, ca 94550.