Finite Difference Methods and Global Errorby O_chemist Tags: difference, error, finite, global, methods 

#1
Feb2612, 11:54 AM

P: 4

I was going through my notes on different finite difference methods and came across something I don't quite understand. I have code that will calculate an approximate solution we can call this U_nm that I define on a grid using h and dt for the change in x and time respectively. Now I have written down the global error is just
e_nm =U_nm  u(xn,tn) where u(xn,tn) is the exact solution evaluated at the gird points. From there we can calculate our rate of convergence So naively I just assumed I could take the solution I calculate and subtract the exact solution at every point take the absolute value. However, I have written something about actually just using e_nm to calculate the initial values as well as boundary conditions and then plugging them back into the finite difference method to calculate all the grid points for all of e_nm. Is this correct or did I perhaps not fully understand what my instructor was saying? (Note we are working with forward, backward and cranknicolson methods) 


Register to reply 
Related Discussions  
Finite element method versus intergrated finite difference for complex geometries?  Differential Equations  6  
Linear & nonlinear shooting and linear & nonlinear finite difference methods  Calculus & Beyond Homework  0  
Numerical methods: Finite difference and spectral methods?  Differential Equations  1  
Finite difference methods  Calculus & Beyond Homework  2  
Finite Difference Methods  Differential Equations  4 