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Question: Calculating values of function of solutions of ODE or PDE in numerical solutions

Question:Calculating values of function of solutions of ODE or PDE in numerical solutions

student_1 305
differential-equation dsolve numeric pdsolve
November 24 2018
0 
restart;
#PDE
PDE := (diff(u(x,y), x,x))-1/x*(diff(u(x, y), x)) -x^2*(diff(u(x,y), y,y))= 2;
BCs:=u(0,t) = 0, u(1,t) = 0;

ICs:=u(x,0) =0, D[2](u)(x,0)=2 ;
num_sol := pdsolve(PDE, {BCs,ICs}, numeric); 
BCs := u(0, t) = 0, u(1, t) = 0;
ICs := u(x, 0) = 0, D[2](u)(x, 0) = 2;
num_sol := pdsolve(PDE, {BCs,ICs}, numeric);

 #ODE
ODE:=diff(y(x),x,x)+16*diff(y(x),x)=0;
 BCs:=y(0) =0, y(2)=3 ;
ode_num_sol:=dsolve({ODE,BCs},numeric);

Suppose that we solved numerically an ODE or PDE like above. 
How to calculate values of function y or u at special values x like analytical solutions?

For example; u(1,1)=? y(1)=? etc.

 

 

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