Taylor Table and Finite Difference Aproximations
Determine the coefficents to a finite differencing scheme
ie. find the coeffs [c1,c2,c3] that are appropriate for the 2nd order
cent. diff. approx. to the first derivative :
(du/dx)[j] = 1/dx*(c1*u[j-1] + c2*u[j] + c3*u[j+1]) + error terms
Inputs:
x - vector containing relative distances to sampling points
ie. for example above would be x=[-1,0,1]
ie. 5 terms full forward: x = [0,1,2,3,4]
ie. 5 terms central : x = [-2,-1,0,1,2]
derv - order of the derivative to approximate
Ouputs:
c - the coefficients you're looking for!
T optional output matrix showing the Taylor Table coefficents
errOrder - lowest order of higher order terms
(order of accuracy, ie. H.O.T. = O(dx^2) is 2nd order)
Taylor table matrix output is ordered similarly to:
http://people.nas.nasa.gov/~pulliam/Classes/New_notes/Taylor_Tables.pdf
Cite As
Brandon Lane (2024). Taylor Table and Finite Difference Aproximations (https://www.mathworks.com/matlabcentral/fileexchange/29297-taylor-table-and-finite-difference-aproximations), MATLAB Central File Exchange. Retrieved .
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