Second Order Derivative using Taylor Table Method

Objective: Derivation: (1) Central Difference Scheme: For Central difference scheme the double derivative can be written as follows `(d^2y)/dx^2=af(i-2)+bf(i-1)+cf(i)+df(i+1)+ef(i+2).......................[I]` Using Taylor Series we can expand the above equation as follows `af(i-2)=(f(i)-2Deltaxf\'(i)+((2Deltax)^2f\'\'(i))/(2!)-((2Deltax)^3f^(iii)(i))/(3!)+((2Deltax)^4f^(iv)(i))/(4!))a`…