Solving a system of second order tightly coupled nonlinear ODE with six initial conditions in Matlab
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I am solving a problem from fluid dynamics; in particular tightly coupled nonlinear ordinary differential equations. The following is a scaled-down version of my actual problem.
I have solved system of coupled odes many times in the past but this case is different since double derivatives of one variable depends on the double derivative of another variable. How do I implement it in ode45? I need 3 x 2 = 6 plots of x, x-dot and x-ddot versus time for t, 0 to 2. All required initial conditions have zero values.
Any help will be highly appreciated. If the ODEs had no last terms of double derivatives, I would have done it myself.
matlab numerical-methods ode scientific-computing numerical-integration
asked Nov 11 at 16:25
Vikash
319
add a comment |
up vote
0
down vote
favorite
I am solving a problem from fluid dynamics; in particular tightly coupled nonlinear ordinary differential equations. The following is a scaled-down version of my actual problem.
I have solved system of coupled odes many times in the past but this case is different since double derivatives of one variable depends on the double derivative of another variable. How do I implement it in ode45? I need 3 x 2 = 6 plots of x, x-dot and x-ddot versus time for t, 0 to 2. All required initial conditions have zero values.
Any help will be highly appreciated. If the ODEs had no last terms of double derivatives, I would have done it myself.
matlab numerical-methods ode scientific-computing numerical-integration
asked Nov 11 at 16:25
Vikash
319
I think this question fits better on math.stackexchange.com
– rinkert
Nov 11 at 17:54
Posted there, not of much help.
– Vikash
Nov 11 at 18:32
Or, can anyone please help me with the solution of a much simpler problem: postimg.cc/9z7LXg8B
– Vikash
Nov 12 at 9:15
Have you tried simply substituting the values for the second derivatives into the expressions? I suggest maybe trying a convenient change of variables, such asu=(x_1+x_2)andv=(x_1-x_2).
– Joey Dumont
Nov 12 at 17:01
I have solved the problem. Thank you all so much for helping me fix this problem. :)
– Vikash
Nov 13 at 15:16
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I am solving a problem from fluid dynamics; in particular tightly coupled nonlinear ordinary differential equations. The following is a scaled-down version of my actual problem.
I have solved system of coupled odes many times in the past but this case is different since double derivatives of one variable depends on the double derivative of another variable. How do I implement it in ode45? I need 3 x 2 = 6 plots of x, x-dot and x-ddot versus time for t, 0 to 2. All required initial conditions have zero values.
Any help will be highly appreciated. If the ODEs had no last terms of double derivatives, I would have done it myself.
matlab numerical-methods ode scientific-computing numerical-integration
asked Nov 11 at 16:25
Vikash
319
I am solving a problem from fluid dynamics; in particular tightly coupled nonlinear ordinary differential equations. The following is a scaled-down version of my actual problem.
I have solved system of coupled odes many times in the past but this case is different since double derivatives of one variable depends on the double derivative of another variable. How do I implement it in ode45? I need 3 x 2 = 6 plots of x, x-dot and x-ddot versus time for t, 0 to 2. All required initial conditions have zero values.
Any help will be highly appreciated. If the ODEs had no last terms of double derivatives, I would have done it myself.
matlab numerical-methods ode scientific-computing numerical-integration
matlab numerical-methods ode scientific-computing numerical-integration
asked Nov 11 at 16:25
Vikash
319
asked Nov 11 at 16:25
Vikash
319
edited Nov 11 at 17:59
asked Nov 11 at 16:25
Vikash
319
asked Nov 11 at 16:25
Vikash
319
asked Nov 11 at 16:25
Vikash
319
319
I think this question fits better on math.stackexchange.com
– rinkert
Nov 11 at 17:54
Posted there, not of much help.
– Vikash
Nov 11 at 18:32
Or, can anyone please help me with the solution of a much simpler problem: postimg.cc/9z7LXg8B
– Vikash
Nov 12 at 9:15
Have you tried simply substituting the values for the second derivatives into the expressions? I suggest maybe trying a convenient change of variables, such asu=(x_1+x_2)andv=(x_1-x_2).
– Joey Dumont
Nov 12 at 17:01
I have solved the problem. Thank you all so much for helping me fix this problem. :)
– Vikash
Nov 13 at 15:16
add a comment |
I think this question fits better on math.stackexchange.com
– rinkert
Nov 11 at 17:54
Posted there, not of much help.
– Vikash
Nov 11 at 18:32
Or, can anyone please help me with the solution of a much simpler problem: postimg.cc/9z7LXg8B
– Vikash
Nov 12 at 9:15
Have you tried simply substituting the values for the second derivatives into the expressions? I suggest maybe trying a convenient change of variables, such asu=(x_1+x_2)andv=(x_1-x_2).
– Joey Dumont
Nov 12 at 17:01
I have solved the problem. Thank you all so much for helping me fix this problem. :)
– Vikash
Nov 13 at 15:16
I think this question fits better on math.stackexchange.com
– rinkert
Nov 11 at 17:54
I think this question fits better on math.stackexchange.com
– rinkert
Nov 11 at 17:54
Posted there, not of much help.
– Vikash
Nov 11 at 18:32
Posted there, not of much help.
– Vikash
Nov 11 at 18:32
Or, can anyone please help me with the solution of a much simpler problem: postimg.cc/9z7LXg8B
– Vikash
Nov 12 at 9:15
Or, can anyone please help me with the solution of a much simpler problem: postimg.cc/9z7LXg8B
– Vikash
Nov 12 at 9:15
Have you tried simply substituting the values for the second derivatives into the expressions? I suggest maybe trying a convenient change of variables, such as
u=(x_1+x_2) and v=(x_1-x_2).– Joey Dumont
Nov 12 at 17:01
Have you tried simply substituting the values for the second derivatives into the expressions? I suggest maybe trying a convenient change of variables, such as
u=(x_1+x_2) and v=(x_1-x_2).– Joey Dumont
Nov 12 at 17:01
I have solved the problem. Thank you all so much for helping me fix this problem. :)
– Vikash
Nov 13 at 15:16
I have solved the problem. Thank you all so much for helping me fix this problem. :)
– Vikash
Nov 13 at 15:16
add a comment |
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I think this question fits better on math.stackexchange.com
– rinkert
Nov 11 at 17:54
Posted there, not of much help.
– Vikash
Nov 11 at 18:32
Or, can anyone please help me with the solution of a much simpler problem: postimg.cc/9z7LXg8B
– Vikash
Nov 12 at 9:15
Have you tried simply substituting the values for the second derivatives into the expressions? I suggest maybe trying a convenient change of variables, such as
u=(x_1+x_2)andv=(x_1-x_2).– Joey Dumont
Nov 12 at 17:01
I have solved the problem. Thank you all so much for helping me fix this problem. :)
– Vikash
Nov 13 at 15:16