How to specify boundary conditions for solution of ODes

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saheed
saheed 2014-9-18
评论： saheed 2014-9-18
Hi everyone,
How can I specify boundary conditions in a matrix to solve the ODE system with the following dsolve command syntax?
syms x1(t) x2(t).....xN(t)
A = [a1 a2....aN; b1 b2...bN;...;d1 d2....dN];
B = [t1; t2;...;tN];
Y = [x1; x2;...;xN];
S = dsolve(diff(Y) == A*Y + B);

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回答（1 个）

Mischa Kim
Mischa Kim 2014-9-18
编辑：Mischa Kim 2014-9-18
saheed, see e.g.
syms R L C Uc(t)
% Define first and second derivatives for Uc
DUcDt = diff(Uc);
D2UcDt2 = diff(Uc,2);
% Perturbation input (or RHS): change input to dirac(t), t, etc.
Uin = 1;
% Define differential equation for linear RLC circuit
RLC_DE = L*C*D2UcDt2 + R*C*DUcDt + Uc == Uin;
% Set initial conditions
Uc0 = Uc(0) == 0;
DUc0 = DUcDt(0) == 0;
% Solve differential equation and display
Uc_sym = dsolve(RLC_DE, Uc0, DUc0);
display(['Uc(t) = ',char(10),char(Uc_sym),char(10)])
Alternatively, check out this example in the documentation.
  1 个评论
saheed
saheed 2014-9-18
Thanks Kim but actually I have tried this syntax you specified but I got error because I need to specify the differential terms A, Y and B in
S = dsolve(diff(Y) == A*Y + B);
as matrices and vectors respectively. So the problem still remains if I specify the conditions of [x1; x2;...;xN] in
Y = [x1; x2;...;xN];
as x1(0)==0, x2(0)==0
just like you suggested. Any further suggestion is highly welcomed.

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