Second Order Numerical Integration w/ Neumann Boundary Conditions

In summary, The person is asking for help with running a numeric integration for a nonlinear second order ODE with Neumann B.C. They have started programming Runge Kutta 4 but are stuck without a boundary condition. They are looking for guidance or a text that discusses this problem and recommend checking the Numerical Recipe website for older versions of the book in pdf format.
  • #1
a2009
25
0
I hope this is the right place to post this question.

I'm trying to figure out how to run a numeric integration for a nonlinear second order ODE with Neumann B.C.

I've started programming up Runge Kutta 4, but clearly without a boundary condition on the function, but only on its derivative I'm stuck.

If anyone could point me in the right direction, or refer me to a text that discusses this problem I'd really appreciate it.
 
Physics news on Phys.org
  • #2
I can add more to this later. But for now check the Numerical Recipe website. www.nr.com Check in the section that has the older versions of the book in pdf format.
 

1. What is second order numerical integration?

Second order numerical integration is a method for approximating the definite integral of a function using numerical techniques. It involves dividing the interval of integration into smaller subintervals and using a second order polynomial to approximate the curve of the function within each subinterval.

2. How is second order numerical integration used in practice?

Second order numerical integration is commonly used in scientific and engineering fields where precise calculations of integrals are needed. It is particularly useful for solving differential equations and other complex mathematical problems.

3. What are Neumann boundary conditions?

Neumann boundary conditions are a type of boundary condition used in mathematical models where the value of the derivative of a function is specified at the boundary. This means that the slope or rate of change of the function is known at the boundary.

4. Why are Neumann boundary conditions important in second order numerical integration?

Neumann boundary conditions are important in second order numerical integration because they provide additional information about the behavior of the function at the boundary. This can improve the accuracy of the numerical integration by allowing for a more precise approximation of the curve at the boundary.

5. What are some common methods for implementing second order numerical integration with Neumann boundary conditions?

Some common methods for implementing second order numerical integration with Neumann boundary conditions include the trapezoidal rule, Simpson's rule, and the midpoint rule. These methods involve using a combination of the function values and their derivatives at specific points within each subinterval to approximate the integral.

Similar threads

I The diffusion equation with time-dependent boundary condition
    • Differential Equations
Replies
8
Views
2K
A Determine PDE Boundary Condition via Analytical solution
    • Differential Equations
Replies
1
Views
2K
Neumann Boundary Conditions using FTCS on the Heat Equation
    • Differential Equations
Replies
1
Views
4K
Q about Poisson eqn w/ Neumann boundary conditions as in Jackson
    • Differential Equations
Replies
5
Views
1K
A Discretization for a fourth-order PDE (and solution)
    • Differential Equations
Replies
2
Views
2K
A Numerical evolution of Einstein-Boltzmann equations in cosmology
    • Cosmology
Replies
2
Views
366
Neumann Condition on Curved Boundary using Finite Difference
    • Differential Equations
Replies
1
Views
3K
A Numerical solution for a two dimensional 3rd order nonlinear diff. eq.
    • Differential Equations
Replies
1
Views
2K
I Resolution of a PDE with second order Runge-Kutta
    • Differential Equations
Replies
6
Views
3K
Solving PDEPE without boundary conditions? heat transfer
    • Differential Equations
Replies
3
Views
4K

Hot Threads

Recent Insights

Back
Top