Use the Fourier method (let U₁₁j = eiwxi . û¹) to discuss the stability of the explicit forward difference method Ui,j+1 = (1 + λ)Uį‚j — λUi+1‚j ut + aux = 0 for the conservation law At where λ = a- Ax

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A: In mathematics, an inverse function is a function that "reverses" another function: if the function…

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A: We solve the given DE  y"-3y'+2y=e3t.......(1) y(0)=y'(0)=0......(2)

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A: Laplace transferom of the function

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A: Consider the provided question,

Q: Find the Fourier Transforms of the indicated function: f (x) = e-3x for x > 0 and f (x) = e2x for x…

A: We have,fx=e-3xx>0e2xx<0 To Do: Find the Fourier Transform of the given function.

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Q: pload answer sheets Find the Laplace transformation of H(t-4)e“-4)

A: Solution is given below:

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A: Formula used: 1. Lft-aHt-a=e-asFs2. Ly''=s2Lyt-sy0-y'03. Ly'=sLyt-y0 Consider the given initial…

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Q: Determine the Laplace transform o sin (8t + 붕). +64 -a +(a) #() +64 +64 O 43 #() 2+64 O 4v3 7+64…

A: We need to find Laplace transform of sin8t+116π Here we will us the following formulas-…

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Q: 8. Solve using Laplace transform: y" + 2y – 3y = 8e¬t + 8 (t – ), y(0) = 3, y' (0) = –5.

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A: We have to solve the given differential equations using Laplace transform.

Q: dy - 4 - 5y = dy -3t sin(4t) ; y (0) = 3, y (0) = 10 dt2

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Q: Find the Laplace transforms of the functions. f(t) = Cos^2(2t)

A: Let ft=cos22tTo find: Laplace transform of the function ft.

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A: If L-1Fs=ft, then L-1Fs-a=eatft. It is known that: L-1as2+a2=sinat and L-1n!sn+1=tn.

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A: This is a question of Fourier Analysis.

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