Solve the question fully parts a,b,c and d and include the requiredcode. Clearly show each step and explain. DO NOT USE ANSWERS FOUNDON CHEGG AND REPOSTS AND DO NOT ANSWER QUESTION IF YOU CANNOTANSWER FULLY AND PROVIDE REQUIRED CODE. YOU WILL BE REPORTED!!!!!!

9. Consider a laterally insulated nnetal bar of length L = 1, which satisfies the heat equation Suppose that the ends of the bar are kept at temperature u0°C and the temperature in the bar at t = 0, u(0,x) = sinmz (a) Using an explicit method with different meshes h to solve the equation and find 1, t 2. t 3.t the numerical solutions, then plot the solutions for t := 0, t and t = 5 in the same figure 4 (b) Using an implicit method with different meshes h to solve the equation and find the numerical solutions, then plot the solutions for t = 0, t = 1, t = 2, t = 3, t = 4 and t = 5 in the same figure. (c) Using Crank-Nicolson method with different meshes h to solve the equation and 2, t find the numerical solutions, then plot the solutions for t = 0,t = 1, t 3, t = 4 and t = 5 in the same figure. (d) Making your discussion for these three methods with different size of h 6 The exact solution for this problem is u(t, z) = sin(nz)e-rap which can be used to compare with your numerical solutions. Show transcribed image text

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