Post by matthorr on Sept 10, 2015 17:37:31 GMT
Construct a Taylor table for:
\( a_0(u_{xx})_{j −1} + (u_{xx})_j + a_2(u_{xx})_{j +1} = \frac{1}{\Delta x^2} (b_0u_{j −1} + b_1u_j + b_2u_{j +1})\quad + ? \)
and find the optimum value for the parameters and the resulting Taylor series error, \(er_t\). What is the order of the method? Is this type of method compact? Is it central /backward or forward? (Hint from Slides?) How are \(a_0\) and \(a_2\) related? \(b_0\) and \(b_2\) related?
\( a_0(u_{xx})_{j −1} + (u_{xx})_j + a_2(u_{xx})_{j +1} = \frac{1}{\Delta x^2} (b_0u_{j −1} + b_1u_j + b_2u_{j +1})\quad + ? \)
and find the optimum value for the parameters and the resulting Taylor series error, \(er_t\). What is the order of the method? Is this type of method compact? Is it central /backward or forward? (Hint from Slides?) How are \(a_0\) and \(a_2\) related? \(b_0\) and \(b_2\) related?