This preview shows page 1. Sign up to view the full content.
Unformatted text preview: problem gives an O ( h 2 ) LTE provided the the solution is at least C 4 . The LTE may be lower order because the solution is not C 4 or because we use a lower order discretization at some points. (a) Suppose that the LTE is O ( h p ) at the Frst grid point ( x 1 = h ). What eect does this have on the error? What is the smallest value of p that gives a second order accurate error? Hint: Use equation (2.46) from LeVeque to aid in your argument. (b) Suppose that the LTE is O ( h p ) at an interior point (i.e. a point that does not limit to the boundary as h 0). What eect does this have on the error? What is the smallest value of p that gives a second order accurate error? (c) Verify the results of your analysis from parts (a) and (b) using numerical tests. 1...
View Full
Document
 Fall '11
 Wiley
 Math, Differential Equations, Equations

Click to edit the document details