Implicit finite difference method

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SUMMARY

The discussion centers on the implementation of the implicit finite difference method for solving the wave equation, specifically using a C program. The participants confirm that at step 1, the index \( j \) should range from 1 to \( J-1 \) to ensure all values are defined, avoiding undefined values at the boundaries. They also discuss the formulation of the linear system to solve for \( W_j^{n+1} \) and the calculation of the vector \( b \) used in this system. Errors in the approximations are analyzed, and the correct implementation of the function to compute \( b \) is debated.

PREREQUISITES
  • Understanding of the wave equation and its boundary conditions
  • Familiarity with implicit finite difference methods
  • Proficiency in C programming, particularly with arrays and numerical methods
  • Knowledge of linear algebra for solving systems of equations
NEXT STEPS
  • Implement error-checking mechanisms in the C program for boundary conditions
  • Explore numerical stability in implicit finite difference methods
  • Learn about optimization techniques for solving linear systems in numerical simulations
  • Investigate alternative numerical methods for solving partial differential equations
USEFUL FOR

Mathematicians, computational physicists, and software developers working on numerical simulations of wave phenomena or similar partial differential equations.

  • #31
I like Serena said:
Yep. That is correct.

Great! (Yes) Thank you for your help! (Happy)

I like Serena said:
Btw, any reason that the return value is "void *" instead of "void"?
And that you execute "pointer++" when you make no use of the incremented value?

I used pointers to return the array and use it in the main function..
 

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