Higher order difference expressions

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SUMMARY

The discussion focuses on deriving a finite difference expression for the sixth order derivative in the context of numerical solutions to differential equations using the finite difference method. The user initially attempted to create this expression using Mathematica 6 but encountered errors in the solution. The term "sixth order derivative in h^2" refers to the error order being proportional to the square of the step size, denoted as O(h²).

PREREQUISITES
  • Understanding of finite difference methods
  • Familiarity with differential equations
  • Knowledge of numerical analysis concepts
  • Experience with Mathematica 6 or similar computational tools
NEXT STEPS
  • Research finite difference expressions for higher order derivatives
  • Learn about error analysis in numerical methods
  • Explore advanced features of Mathematica 6 for numerical solutions
  • Study the implications of step size on numerical accuracy
USEFUL FOR

Mathematicians, numerical analysts, and engineers working on solving differential equations using numerical methods, particularly those interested in higher order finite difference techniques.

karaali
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Hello. I need finite difference expression of sixth order derivative in h^2. I derived it using Mathematica 6 but when I use the expression there appear a problem. Solution is wrong. I check everythin and realized that only i m not sure about that expression. I ll be appreciated if you help. Thanks in advance.
 
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I don't know what you mean by " sixth order derivative in h^2".
 
Hi. Let me explain.

I have a differential equation and try to solve it using finite difference method. Differential equation has sixth order derivative of dependent variable. So; i need difference expression for that derivative. "h" is the step size and saying " sixth order derivative in h^2" i mean the order of the error is square of step size.( O(h2) )
 

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