Q5) Use 4th-order Runge Kutta method hf(tn, Vn), 1 hf (tn + h, Yn +5k kz kg = hf (tn +h, yn + k4 = hf(tn + h, Yn + k3), 1 Un +1 Yn + (kı + 2k2 + 2k3 + ka). with h=1/4 to compute approximate value of y(1) for the initial-value problem below. y'(1) = y(1+e"), y(0) =1 Fill in the Table below. k, k. x100% 1 1/4 2 1/2 3/4 4 1

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Q: Solution: y1 = 2.513274123; y2 = 1.814517822; y3 = 1.216364496

A: Here, initial condition is given at x = 1.Therefore, start with x0 = 1.Given equation is:

Q: 4+ Out X=U -3n,t Ox-2n3=6 + Yx2-2n3

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Q: 3. Using Jacobi Method, obtain the solution to the system 21 + 522 + 33 = 30 3x1 + 7x2 + 13x3 = 80…

A: Let us solve the system of linear equations using Jacobi Method in the next steps.

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A: Given, The system of equation is, 4.5a -0.5b = 1, a -3.5b = -1.

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Q: Find the solution using LU Decomposition: 7x + 5y − 3z = 16 3x − 5y + 2z = −8 5x + 3y − 7z = 0

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Q: (d) Fourth-order Runge-Kutta (RK) method with h = 0.5.

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Q: Solution: y1 = 1.450000000; y2= 2:085625000; y3 = 3:079099746

A: Here, initial condition is given at x = 2.Therefore, start with x0 = 2.Given equation is:

Q: 2.3 Why is the Runge-Kuuta method more accurate compared to the Euler's

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Q: (c) Manipulating the forward Euler method written for the step sizes h, h/2, and h/3, apply…

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Q: What is the approximate value of x in the system 20x + y – 2z = 17 3x + 20y – z = -18 2x – 3y + 20z…

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Q: Test whether the Gauss-Seidel iteration converges for the system 10x +2y + z = 22 x+10y z = 22 -2x +…

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Q: Use the backward Euler method with h = 0.1 y'(t) + 1000cos(y(t))-100t = 0 y(0) = -0.5   find y(2)

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Q: 7. Solve x1,x2,x3,x4 using LU or Naïve Gauss method exz + V2x3 – V3x4 = /TI, x?x, + exz - e²x3 + x4…

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Q: Use the Newton Raphson Method with X©)=[-1 -2 1]T to approximate the solution to the given nonlinear…

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