Iteration algorithm for finding better approximation in Shooting method for solving BVP











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Good day, everyone. Basically , the problem I am given is to solve the system of differential equations with 4 equations, and I have two initial values, and two boundary conditions. Following the Shooting method theory, I supply my system with two guesses for missing initial values, solve the system using Runge-Kutta 4th order, and obtain some values for functions, which are not right based on my boundary conditions.The question is how to iterate my system of approximations for initial values, to obtain right initial guesses? If I had only one value to be found by this method, it would be easy, by just implementing some form of linear interpolation, squeezing down the solution from two ends. But since there are two values guessed, it is not working anymore. Any ideas would be greatly appreciated.






numerical-methods runge-kutta-methods







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  • My functions are like this: $dot x_1(t) = x_2(t)$, $dot x_2(t) = p_2(t)-sqrt 2 x_1(t)e^{-alpha t}$, $dot p_1(t) = sqrt 2 p_2(t)e^{-alpha t}+x_1(t)$, $dot p_2(t) = -p_1(t)$ with initial and boundary values of: $x_1(0)=1,p_2(0)=0 p_1(1)=0,p_2(1)=0$
    – Farid Hasanov
    23 hours ago















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Good day, everyone. Basically , the problem I am given is to solve the system of differential equations with 4 equations, and I have two initial values, and two boundary conditions. Following the Shooting method theory, I supply my system with two guesses for missing initial values, solve the system using Runge-Kutta 4th order, and obtain some values for functions, which are not right based on my boundary conditions.The question is how to iterate my system of approximations for initial values, to obtain right initial guesses? If I had only one value to be found by this method, it would be easy, by just implementing some form of linear interpolation, squeezing down the solution from two ends. But since there are two values guessed, it is not working anymore. Any ideas would be greatly appreciated.






numerical-methods runge-kutta-methods







share|cite|improve this question







New contributor




Farid Hasanov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.




















  • My functions are like this: $dot x_1(t) = x_2(t)$, $dot x_2(t) = p_2(t)-sqrt 2 x_1(t)e^{-alpha t}$, $dot p_1(t) = sqrt 2 p_2(t)e^{-alpha t}+x_1(t)$, $dot p_2(t) = -p_1(t)$ with initial and boundary values of: $x_1(0)=1,p_2(0)=0 p_1(1)=0,p_2(1)=0$
    – Farid Hasanov
    23 hours ago













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0
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up vote
0
down vote

favorite











Good day, everyone. Basically , the problem I am given is to solve the system of differential equations with 4 equations, and I have two initial values, and two boundary conditions. Following the Shooting method theory, I supply my system with two guesses for missing initial values, solve the system using Runge-Kutta 4th order, and obtain some values for functions, which are not right based on my boundary conditions.The question is how to iterate my system of approximations for initial values, to obtain right initial guesses? If I had only one value to be found by this method, it would be easy, by just implementing some form of linear interpolation, squeezing down the solution from two ends. But since there are two values guessed, it is not working anymore. Any ideas would be greatly appreciated.






numerical-methods runge-kutta-methods







share|cite|improve this question







New contributor




Farid Hasanov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











Good day, everyone. Basically , the problem I am given is to solve the system of differential equations with 4 equations, and I have two initial values, and two boundary conditions. Following the Shooting method theory, I supply my system with two guesses for missing initial values, solve the system using Runge-Kutta 4th order, and obtain some values for functions, which are not right based on my boundary conditions.The question is how to iterate my system of approximations for initial values, to obtain right initial guesses? If I had only one value to be found by this method, it would be easy, by just implementing some form of linear interpolation, squeezing down the solution from two ends. But since there are two values guessed, it is not working anymore. Any ideas would be greatly appreciated.






numerical-methods runge-kutta-methods




numerical-methods runge-kutta-methods






share|cite|improve this question







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Farid Hasanov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|cite|improve this question







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Farid Hasanov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









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Farid Hasanov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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Farid Hasanov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Farid Hasanov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.












  • My functions are like this: $dot x_1(t) = x_2(t)$, $dot x_2(t) = p_2(t)-sqrt 2 x_1(t)e^{-alpha t}$, $dot p_1(t) = sqrt 2 p_2(t)e^{-alpha t}+x_1(t)$, $dot p_2(t) = -p_1(t)$ with initial and boundary values of: $x_1(0)=1,p_2(0)=0 p_1(1)=0,p_2(1)=0$
    – Farid Hasanov
    23 hours ago


















  • My functions are like this: $dot x_1(t) = x_2(t)$, $dot x_2(t) = p_2(t)-sqrt 2 x_1(t)e^{-alpha t}$, $dot p_1(t) = sqrt 2 p_2(t)e^{-alpha t}+x_1(t)$, $dot p_2(t) = -p_1(t)$ with initial and boundary values of: $x_1(0)=1,p_2(0)=0 p_1(1)=0,p_2(1)=0$
    – Farid Hasanov
    23 hours ago
















My functions are like this: $dot x_1(t) = x_2(t)$, $dot x_2(t) = p_2(t)-sqrt 2 x_1(t)e^{-alpha t}$, $dot p_1(t) = sqrt 2 p_2(t)e^{-alpha t}+x_1(t)$, $dot p_2(t) = -p_1(t)$ with initial and boundary values of: $x_1(0)=1,p_2(0)=0 p_1(1)=0,p_2(1)=0$
– Farid Hasanov
23 hours ago




My functions are like this: $dot x_1(t) = x_2(t)$, $dot x_2(t) = p_2(t)-sqrt 2 x_1(t)e^{-alpha t}$, $dot p_1(t) = sqrt 2 p_2(t)e^{-alpha t}+x_1(t)$, $dot p_2(t) = -p_1(t)$ with initial and boundary values of: $x_1(0)=1,p_2(0)=0 p_1(1)=0,p_2(1)=0$
– Farid Hasanov
23 hours ago















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