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truncerror

-              v1
+              v2
 Replacing derivatives in differential equations with finite difference approximations, gives a system of algebraic equations that can be solved numerically. To analyse the error in this case, we now need a "local truncation error" at each grid point as well as some handle on the "global error" over the entire mesh.
+Replacing derivatives in differential equations with finite difference approximations replaces the original diff-eq problem with a system of algebraic equations. To analyse the error in this case, we need the concepts of "local truncation error" at each grid point, as well as some handle on the "global error" over the entire mesh.
+= Local truncation error =
+= Local truncation error (LTE)=
+LTE is a measure of how well a solution to a particular ODE satisfies the finite difference approximation of that ODE. Say we discretize the following equation:
+The concept of LTE is illustrated with the following example. Suppose we replace the 2nd derivative of the following ODE
+and discretize the functions over some finite number of grid points:
+with the finite difference version