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where s is a variable along the length of the cable. (a) Applying the Runge-Kutta method to solve the equation (2), where w 0.12 kN/m, A-A-0,200 m, and a 50 m. Let the initial conditions be y 0 at ® FA 0, iterate T, value until в is within 99.9% of 50 m. of the Runge-Kutta method ( remains equal to 0.12 kN/m)? ot her methods if possible. (b) How could the problem be solved ifFA = 100 m and yA = 25 m by application (e) Making a discussion about mumerical results with different mesh steps and with 7. The equntion has the analytical solution yt) tant. The tangent function is infinite at 2 (a) Write your program by using both Euler and Runge-Kutta method to solve this 1.6, and compare the results of the (b) What is the behaviour of the Runge-Kutta fourth order method when used be (e) Compare the results from your codes and make comments on the behaviour initial value problem between t-0 and t program with the analytical solution tween t-0 and t 16 change with step sizes. 8. Given the following non-linear boundary value problem (a) Use the shooting method to approximate solution (b) Use finite diference to approocimate solution (e) Plot the approximate solutions together with the exact solution yit)a and discuss your results with both methods 9. Here is a typical steewly-state beat Bow problem. Consider a thin steel plate to be a 10 x 20 (em) rectangle. If one side of the 10 em edge is held at 100PC and the other three edges are beld at 0C, what are the steady-state temperature at interior points? We can state the problem mathematically in this way if we assume that heat flows only in the r and y directions: Find u(r,v) (temperature) such that with boundary conditions u(E,0)-0 u(z, 10) = 0 (0,y) 0 (20,V) = 100 We replace the differential equation by a difference equation

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