Can Matlab ODE solver solve this problem

2017 11 29
1 个回答
更新时间：2021 8 20
2 次查看（30 天）

0 个投票

Can Matlab ODE solver solve this problem

4 个评论
显示 2更早的评论 隐藏 2更早的评论

Torsten
Torsten 2017-11-29
Why are there two independent variables (eta and lambda) ?
Best wishes
Torsten.
WEI JIN
WEI JIN 2017-11-29
Yes, eta and lambda are two different independent variables. The function to be solved q(eta) only depends on eta, and the function p(lambda) only depends on lambda. Can ordinary differential equation solver solve this problem? Or still consider the system as a partial differential equation with two independent variables, the two functions to be solved depends on both independent variables, i.e., q(eta,lambda), p(eta,lambda), with the condition that q^{\prime}(\lambda) =0 and p^{\prime}(\eta)=0.
Jan
Jan 2017-11-29
编辑：Jan 2017-11-29
It depends on what eta, lambda, q, p, q' and p', f and g are. Please provide any details. If the problem can be solved at all (numerically or symbolically?), then it is possible with Matlab also - most likely.
WEI JIN
WEI JIN 2017-11-29
These are two implicit ordinary differential equations, so the function form f and g are known. The unknown functions to be solved are q and p. The question is can we use ODE solver to numerically solve the function q=q(eta) and p=p(lambda) that satisfy the two equations.

回答（1 个）

Torsten
Torsten 2017-11-29

0 个投票

Given p(lambda_i) and q(eta_i), you can determine p(lambda_i+delta_lambda) and q(eta_i+delta_eta) by solving the system of equations
f(eta_i+delta_eta,lambda_i+delta_lambda,q(eta_i+delta_eta),p(lambda_i+delta_lambda),(q(eta_i+delta_eta)-q(eta_i))/delta_eta,(p(lambda_i+delta_lambda)-p(lambda_i))/delta_lambda)=0
g(eta_i+delta_eta,lambda_i+delta_lambda,q(eta_i+delta_eta),p(lambda_i+delta_lambda),(q(eta_i+delta_eta)-q(eta_i))/delta_eta,(p(lambda_i+delta_lambda)-p(lambda_i))/delta_lambda)=0
using "fsolve", e.g.
So starting from p(lambda_start) and q(eta_start) (initial values), you can integrate your system up to specified values for lambda_end and eta_end.
Look up "method of characteristics" for more details.
Best wishes
Torsten.

此问题已关闭。

标签

提问:

WEI JIN
WEI JIN
2017-11-29

关闭：

MATLAB Answer Bot
MATLAB Answer Bot
2021-8-20

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by