(Solved): 6. The Crank-Nicolson + central difference scheme for heat equation du = vu+ is centered in ...

6. The Crank-Nicolson + central difference scheme for heat equation du = v?²u+ƒ is centered in both space and time. Define its local truncation error ? by u(2i,©n+1) ? u(i, tn) At u(2i_1,tn) — 2u(i,tn) +u(2i+l,tn) h² = V // ( 2 + u(2i_1,€n+1) ? 2u(2i,©n+1) +u(2;+1,$n+1) h² littlnt)) + f (xi, tn+ 3) + T7. Assume the function is smooth enough. Determine the constants a and ß so that T? = O(Atª +h³³). [5 marks]