Second Order Numerical Integration w/ Neumann Boundary Conditions

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SUMMARY

This discussion focuses on implementing numerical integration for a nonlinear second order ordinary differential equation (ODE) with Neumann boundary conditions. The user is currently utilizing the Runge-Kutta 4 method but encounters challenges due to the boundary condition being applied to the derivative rather than the function itself. The Numerical Recipes website is recommended as a resource for further guidance on this topic.

PREREQUISITES
  • Understanding of nonlinear second order ordinary differential equations (ODEs)
  • Familiarity with Neumann boundary conditions
  • Knowledge of the Runge-Kutta 4 numerical integration method
  • Basic proficiency in programming for numerical methods
NEXT STEPS
  • Study the implementation of Neumann boundary conditions in numerical methods
  • Explore advanced topics in nonlinear ODEs
  • Review the Numerical Recipes book, particularly the sections on numerical integration techniques
  • Learn about alternative numerical methods for solving ODEs, such as finite difference methods
USEFUL FOR

Mathematicians, engineers, and computational scientists working on numerical methods for differential equations, particularly those dealing with boundary value problems.

a2009
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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.
 
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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.
 

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