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Explicit Euler Method Given with boundary conditions And initial conditions We obtain the difference method by using the Taylor series to form the difference Quotient Given that, M = 20, N = 100 and π’(π₯, 0) = sin(ππ₯). The exact solution is given by π’(π₯, π‘) = sin(ππ₯) exp (βπ2π‘). The plot using the Explicit Euler method for β = 0, β = 0.25, β = 0.5, β = 0.75, h=1 successively. t h Error= h-t 0 0 0 0.0125 0.025 0.05 0.25 0.2375 0.5 0.475 0.75 0.7 Plot for varying h and t=0.5 with the Explicit Euler method 0.1 1 0.9 0 1 0.25 0.5 0.75 0.0125 0.025 0.05 2 3 4 t Implicit Euler Method Given that Considering again the heat equation, h 1 0.1 5 With the boundary conditions and the initial conditions Given that, M = 20, N = 100 and π’(π₯, 0) = sin(ππ₯). The exact solution is given by π’(π₯, π‘) = sin(ππ₯) exp (βπ2π‘). The plot using the Explicit Euler method with β = 0, β = 0.25, β = 0.5, β = 0.75, h=1 successively. t h Error= h-t 0 0 0 0.0125 0.025 0.05 0.25 0.2375 0.5 0.475 0.75 0.7 Plot of h and t using Implicit Euler method 0 1 0.25 0.5 0.75 0.0125 0.025 0.05 2 3 4 t h 1 0.1 5 0.1 1 0.9 MATLAB CODES % Code for Explicit Euler Method t_0=0; % initial value of time u_0=[1 0]; % initial condition for the solution t_final=0.1; % final value of time h=0.1; % time steps % Call Explicit Euler method % Output is result, which contain [t u] method=input('meth ...
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