Post by matthorr on Sept 10, 2015 17:29:10 GMT
As mentioned in class, sometimes we may want to use the nodal point values of the solution to obtain an intermediate value (interpolation). Use Taylor series analysis for the following point operator approximation to the value at a point two-thirds of the way between \(j\) and \(j+1\):
\( (u)_{j+⅔} = \left(au_{j +1} + bu_j + cu_{j −1}\right)\quad + ? \)
and find the optimum value for the parameters and the resulting Taylor series error, \(er_t\) . What is the order of the method? Please note the following observation: How is this formula related to the interpolation at \(j-⅔\)?
\( (u)_{j+⅔} = \left(au_{j +1} + bu_j + cu_{j −1}\right)\quad + ? \)
and find the optimum value for the parameters and the resulting Taylor series error, \(er_t\) . What is the order of the method? Please note the following observation: How is this formula related to the interpolation at \(j-⅔\)?