level 1
mirror3927
楼主
\[Eta] = 1;
Subscript[\[Tau], s] = 0.5;
R = 0.05;
b = 3;
Num = 5;
Subscript[R, 1] = b - (b - 1)*R;
Subscript[R, 2] = R;
Subscript[R, 3] = 1;
Subscript[R, 4] = R;
Subscript[R, 5] = Num + (Num - 1)*R;
Ux1[\[Xi]_] :=
Subscript[R, 2]*D[Subscript[U1, x2][\[Xi]], {\[Xi], 2}] +
2 (Subscript[U1, x3][\[Xi]] - Subscript[U1, x2][\[Xi]]) - (-\[Eta]*
Subscript[\[Tau], s]);
Ux2[\[Xi]_] :=
Subscript[R, 3]*D[Subscript[U1, x3][\[Xi]], {\[Xi], 2}] +
2 (Subscript[U1, x4][\[Xi]] - 2 Subscript[U1, x3][\[Xi]] +
Subscript[U1, x2][\[Xi]]);
Ux3[\[Xi]_] :=
Subscript[R, 4]*D[Subscript[U1, x4][\[Xi]], {\[Xi], 2}] +
2 (Subscript[U1, x5][\[Xi]] - 2 Subscript[U1, x4][\[Xi]] +
Subscript[U1, x3][\[Xi]]);
Ux4[\[Xi]_] :=
Subscript[R, 5]*D[Subscript[U1, x5][\[Xi]], {\[Xi], 2}] +
2 (Subscript[U1, x4][\[Xi]] - 2 Subscript[U1, x5][\[Xi]]);
DD = DSolve[{Ux1[\[Xi]] == 0, Ux2[\[Xi]] == 0, Ux3[\[Xi]] == 0,
Ux4[\[Xi]] == 0}, {Subscript[U1, x2][\[Xi]],
Subscript[U1, x3][\[Xi]], Subscript[U1, x4][\[Xi]],
Subscript[U1, x5][\[Xi]]}, \[Xi]] // Simplify;
Subscript[U1, b1] = Subscript[U1, x2][\[Xi]] /. DD
解以上微分方程,得到一个通解。
请问有什么办法可以将通解中的常数项参数C[1]-C[8],变为可赋值的未知数C1-C8吗?因为想通过后面的条件求解常数项。
自己摸索了很多方法好像都不太对,希望有大神可以解答!!万分感谢!!!
2021年06月04日 15点06分
1
Subscript[\[Tau], s] = 0.5;
R = 0.05;
b = 3;
Num = 5;
Subscript[R, 1] = b - (b - 1)*R;
Subscript[R, 2] = R;
Subscript[R, 3] = 1;
Subscript[R, 4] = R;
Subscript[R, 5] = Num + (Num - 1)*R;
Ux1[\[Xi]_] :=
Subscript[R, 2]*D[Subscript[U1, x2][\[Xi]], {\[Xi], 2}] +
2 (Subscript[U1, x3][\[Xi]] - Subscript[U1, x2][\[Xi]]) - (-\[Eta]*
Subscript[\[Tau], s]);
Ux2[\[Xi]_] :=
Subscript[R, 3]*D[Subscript[U1, x3][\[Xi]], {\[Xi], 2}] +
2 (Subscript[U1, x4][\[Xi]] - 2 Subscript[U1, x3][\[Xi]] +
Subscript[U1, x2][\[Xi]]);
Ux3[\[Xi]_] :=
Subscript[R, 4]*D[Subscript[U1, x4][\[Xi]], {\[Xi], 2}] +
2 (Subscript[U1, x5][\[Xi]] - 2 Subscript[U1, x4][\[Xi]] +
Subscript[U1, x3][\[Xi]]);
Ux4[\[Xi]_] :=
Subscript[R, 5]*D[Subscript[U1, x5][\[Xi]], {\[Xi], 2}] +
2 (Subscript[U1, x4][\[Xi]] - 2 Subscript[U1, x5][\[Xi]]);
DD = DSolve[{Ux1[\[Xi]] == 0, Ux2[\[Xi]] == 0, Ux3[\[Xi]] == 0,
Ux4[\[Xi]] == 0}, {Subscript[U1, x2][\[Xi]],
Subscript[U1, x3][\[Xi]], Subscript[U1, x4][\[Xi]],
Subscript[U1, x5][\[Xi]]}, \[Xi]] // Simplify;
Subscript[U1, b1] = Subscript[U1, x2][\[Xi]] /. DD
解以上微分方程,得到一个通解。
请问有什么办法可以将通解中的常数项参数C[1]-C[8],变为可赋值的未知数C1-C8吗?因为想通过后面的条件求解常数项。
自己摸索了很多方法好像都不太对,希望有大神可以解答!!万分感谢!!!