Differential equation of second order with two variables
์กฐํ ์: 9 (์ต๊ทผ 30์ผ)
์ด์ ๋๊ธ ํ์
to be solved is the equation ๐ธ๐ผ๐ค4(๐ฅ,๐ก)+๐ ๐คฬ(๐ฅ,๐ก)=0 and this can be solved by expressing ๐ค(๐ฅ,๐ก)= ๐(๐ฅ)โ
๐(๐ก)
for ๐(๐ฅ) we do have this expression ๐๐(๐ฅ)=๐ดโ
[sin(๐๐ ๐ฅ๐ฟ)โsinh(๐๐ ๐ฅ๐ฟ)+sin(๐๐)+sinh(๐๐)cos(๐๐)+cosh(๐๐)โ
(cosh(๐๐ ๐ฅ๐ฟ)โcos(๐๐๐ฅ๐ฟ)) ]
and for ๐๐(๐ก)=๐(0)cos(๐๐ ๐ก)+๐ฬ(0)๐sin(๐๐(๐ก))=๐ถ(0)โ
๐๐๐ (๐๐ ๐ก+๐(0)). Whereas ๐๐ is solved through this equation 1+cos(๐๐)โ
cosh(๐๐)=0
I am guessing that to solve the first differential equation as conditions we can use the three other equations given.
Does anyone has some tipps how this differential equation can be solved?
๋๊ธ ์: 0
๋ต๋ณ (1๊ฐ)
Pranjal Saxena
2023๋
7์ 28์ผ
Hi Florian,
I understand that you want to solve this second order differential equation.
You can use the โSymbolic Math Toolboxโ in MATLAB to do so.
A typical approach to solving higher-order ordinary differential equations is to convert them to systems of first-order differential equations, and then solve those systems.
First you need to convert the second-order differential equation into a system of differential equations that can be solved using the numerical solver โode45โ of MATLAB.
You can refer to the following MATLAB documentations for more information:
I hope this helps.
Warm Regards,
Pranjal.
๋๊ธ ์: 0
์ฐธ๊ณ ํญ๋ชฉ
์นดํ ๊ณ ๋ฆฌ
Help Center ๋ฐ File Exchange์์ Symbolic Math Toolbox์ ๋ํด ์์ธํ ์์๋ณด๊ธฐ
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!