- #1
Necmi
- 10
- 0
u'(1-epsilon(u')^2)=-y
uo(1)=0 u1(1)=0
I need solve this problem with mathematica.
uo(1)=0 u1(1)=0
I need solve this problem with mathematica.
Necmi said:u'(1-epsilon(u')^2)=-y
uo(1)=0 u1(1)=0
I need solve this problem with mathematica.
Thanks.Are you know perturbation method?Mark Harder said:So, you solved the problem by hand, but you have to do it in MMA, for your thesis? Is that correct? I know a little MMA, and I'm willing to look into it, but I can't read the photos of your solution, so I'm going to need some more information. Reading your original post, it looks like you are working with 4 functions - u, u0, u1 and epsilon. Is that right? It seems a little peculiar to me. A more explicit problem statement would be helpful.
Perturbation theory is a mathematical method used to approximate solutions to complex problems by breaking them down into simpler, solvable components. It is especially useful for problems that cannot be solved exactly, such as those involving nonlinear systems or small changes to a known solution.
Perturbation theory works by starting with a known solution to a problem and then introducing a small change or perturbation. The solution is then approximated by considering the perturbation as a small parameter and using a series expansion to find higher-order corrections to the solution. The accuracy of the approximation depends on the size of the perturbation and the number of terms included in the series.
Mathematica is a software program used for mathematical and scientific computing. It is particularly well-suited for performing complex calculations, visualizing data, and solving mathematical problems using built-in algorithms and functions. It is commonly used in fields such as physics, engineering, and economics.
Mathematica has a built-in function called Perturb that can be used to solve perturbation problems. This function takes in the perturbation as a parameter and uses a series expansion to approximate the solution to the problem. It also allows for the inclusion of higher-order corrections and the ability to plot the solution.
One of the main advantages of using Mathematica for perturbation problems is its ability to handle complex calculations and quickly generate accurate solutions. It also has a user-friendly interface and a wide range of built-in functions and algorithms that can be utilized for different types of perturbation problems. Additionally, Mathematica allows for the visualization of solutions, making it easier to interpret and analyze the results.