Fourth order approximation of 2nd order derivative using taylor method

Objective: 4th order approximation of 2nd order derivative 1)central differenicing let number of points=n;order of accuracy=a;order of derivative=o n=a+o-1 therefore n=5; now using taylor table method `(del^2u)/(delx^2)`=af(i-2)+bf(i-1)+cf(i)+d*f(i+1)+e*f(i+2) taylor table then coverting into matrix form `[[1,1,1,1,1],[-2,-1,0,1,2],[2,1/2,0,1/2,2],[-8/6,-1/6,0,1/6,8/6],[16/24,1/24,0,1/24,16/24]]`*`[[a],[b],[c],[d],[e]]`=`[[0],[0],[1],[0],[0]]`…