= дх2 TASK 2 ди The temperature in a laterally insulated bar can be modelled by the heat equation et = k ore at With a b

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i) Set up a numerical method to solve the problem based on the
finite difference method by
subdividing the interval (a,b) in I
subdivisions and defining as :

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= дх2 TASK 2 ди The temperature in a laterally insulated bar can be modelled by the heat equation et = k ore at With a bar of length 1, find a function u (x, t) to express the temperature as a function of time, if the boundary conditions are given by u (0, t) = 0 and u (6, t) = 0, and the initial condition is given by u(x,0) = 3 sin(51x). Let k = 1.
ut = u(xit"), i = 1,...,1 where Xi = a + (i - 1)Ax, Ax = (b - a)/(1 - 1) = and writing the finite difference equation at discrete time steps t=1" where t” = nAt, with a suitably chosen time step At and number of sub-intervals I.
Conduct numerical computation for the conditions given in Task 2. solving for u, i=1, I, n=1,2,.. suitably choosing the interval 4x and the time step At.