Solving forth order nonlinear ode

Some methods for solving non-linear diff.eqs include the shooting method, the finite difference method, and the finite element method.In summary, The conversation discusses the difficulty in finding exact solutions to a non-linear differential equation with its boundary conditions, despite reducing the order of the equation. It suggests using numerical methods such as the shooting method, finite difference method, or finite element method to solve the equation.
  • #1
hamidD
1
0
hello
I want to find exact solution of a nonlinear ode with its boundary conditions . the equation
and its b.cs are written below :

a*y''''+y''' y -y'' y' = 0 y(h/2)=V1 , y(-h/2)=V2 , y'(h/2)=0 , y'(-h/2)=0

where V1 , V2 , a and h are constant .

although with integerating from above equation , the order of ode reduce to 3 but the problem is until unsolveable .

after integrating from above equation we have : a y''' +y'' y -y'^2 =C
where C is constant .
 
Physics news on Phys.org
  • #2
In general, you won't be able to find exact solutions to non-linear diff.eqs; you'll need to solve it numerically.
 

What is a fourth order nonlinear ODE?

A fourth order nonlinear ODE is a type of differential equation that involves the fourth derivative of a function and has nonlinear terms. This means that the function and its derivatives are raised to powers or multiplied together, making it more complex than a linear ODE.

Why is solving fourth order nonlinear ODEs difficult?

Solving fourth order nonlinear ODEs can be difficult because there is no general formula or method that can be applied to all types of equations. Each equation may require a different approach and there is no guarantee that a closed-form solution exists. Additionally, nonlinear terms make the equation more complex and can lead to multiple solutions or no solutions at all.

What are some common techniques for solving fourth order nonlinear ODEs?

Some common techniques for solving fourth order nonlinear ODEs include using power series, substitution methods, numerical methods, and using computer software such as MATLAB or Mathematica. It is also important to simplify the equation as much as possible before attempting to solve it.

What are some real-world applications of fourth order nonlinear ODEs?

Fourth order nonlinear ODEs have a wide range of applications in fields such as physics, engineering, and biology. Some examples include analyzing the motion of a pendulum, modeling the spread of diseases, and predicting the behavior of complex electronic circuits.

What should I keep in mind when solving a fourth order nonlinear ODE?

When solving a fourth order nonlinear ODE, it is important to carefully consider the initial conditions and boundary conditions, as well as the appropriate method to use. It may also be helpful to check for errors or inconsistencies in the equation before attempting to solve it. In some cases, it may be necessary to consult with other experts or conduct further research to fully understand the problem.

Similar threads

I Question about solving linear first order non-homogeneous ODEs
    • Differential Equations
Replies
3
Views
787
I Nonlinear Second Order ODE: Can We Find an Analytical Solution?
    • Differential Equations
Replies
2
Views
2K
I Converting Second Order ODE to Hypergeometric Function
    • Differential Equations
Replies
7
Views
2K
I Fundamental matrix of a second order 2x2 system of ODEs
    • Differential Equations
Replies
2
Views
1K
I Does this ODE have any real solutions?
    • Differential Equations
Replies
11
Views
3K
I Solving Differential Equation Using Reduction of Order
    • Differential Equations
Replies
2
Views
984
A Bessel functions of imaginary order
    • Differential Equations
Replies
2
Views
2K
I How to find the integrating factor? (1st order ODE)
    • Differential Equations
Replies
2
Views
1K
A Nonlinear Wave Equation (Nonlinear Helmholtz)
    • Differential Equations
Replies
1
Views
1K
I Solve second order linear differential equation
    • Differential Equations
Replies
7
Views
1K

Hot Threads

Recent Insights

Back
Top