Consider the following heat conduction problem in a 1D bar

Insulator ot with boundary conditions =0 ox 0 dT dx 1 x=0, t>0 ox and initial condition T(x) = 100cos(-x) t=0, 0 x 1 Write a MATLAB program to solve this problem numerically using an explicit finite difference scheme by dividing the region 0x 1 into 10 intervals. Solve this problem subject to the following conditions -1, -0, I , -0.005, and compare the solution with the exact solution which is given by 4 Plot the numeric solution and the exact solution on the same plot at different timest0.5, 1, 1.5 and 2 seconds. Hint: use a fictitious node at x-0 to implement the dT/dx. The code at his node i l looks like Ta,n+ I) = (alpha*delta, t/delta-r2)*T(i + l ,n)+( 1-2"alpha"delta t/delta-r2) *T(i,n)+(alpha *delta tldelta x*2)*T(i+I,n)