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how to solve set of differential equation Warning: Unable to find explicit solution. > In dsolve (line 190)

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Waqar Ahmed
Waqar Ahmed 2020-3-10
回答： Waqar Ahmed 2020-3-10
syms A1(z) A2(z)
n1=1;
n2=1;
L=100;
deltak=2*pi/L;
ode1 = diff(A1) == i*n1*A1*A2*exp(-i*deltak*z);
ode2 = diff(A2) == i*n2*A1^2*exp(i*deltak*z);
cond1=A(0)==1
cond2=A(1)==0
dsolve([ode1,ode2],[cond1,cond2])
  2 个评论
Walter Roberson
Walter Roberson 2020-3-10
A is not defined in your boundary conditions. Probably A(0) should be A1(0) and A(1) should be A2(0) but I cannot be sure.
Waqar Ahmed
Waqar Ahmed 2020-3-10
the answer is same for the the below question
syms A1(z) A2(z)
n1=1;
n2=1;
L=100;
deltak=2*pi/L;
ode1 = diff(A1) == i*n1*A1*A2*exp(-i*deltak*z);
ode2 = diff(A2) == i*n2*A1^2*exp(i*deltak*z);
cond1=A1(0)==1;
cond2=A2(1)==0;
dsolve([ode1,ode2],[cond1,cond2])

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采纳的回答

Waqar Ahmed
Waqar Ahmed 2020-3-10
This question is solved numerically and the result is gotten as expected using ode45 function

更多回答（1 个）

Walter Roberson
Walter Roberson 2020-3-10
Ignoring the questionable boundary conditions for the moment:
That pair of equations has one closed form solution:
A1(z) = 0
A2(z) = constant that depends on boundary condition
There is also a more general solution that cannot be expressed explicitly -- not really a solution as such, but rather a set of conditions that A1 and A2 would have to satisfy in order for them to be solutions.
  2 个评论
Walter Roberson
Walter Roberson 2020-3-10
Note that your boundary condition of A1(0)=1 rather than A1(0) = 0, rules out the degenerate form.
if the conditon are not been used it does not have even the solution
It has no closed form solution, just a description of what a solution would have to look like. The description looks like
MATLAB is not programmed to be able to find these general descriptions of solutions.
TL;DR: You cannot solve those symbolically.

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