The implicit BTCS scheme is unconditionally stable This was covered in the

# The implicit btcs scheme is unconditionally stable

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Is incorrect. The implicit BTCS scheme is unconditionally stable. (This was covered in the lectureon von Neumann stability analysis where we compared FTCS and BTCS.)(ii)Is incorrect. An infinite number of Fourier modes are needed to encode a square wave initialcondition (i.e. a square wave). If the solution had only 1 mode it would necessarily mean the initialcondition was a single sinusoidal mode – and a square wave is clearly not. Remember that aFourier series is used to represent a function, and a function with sharp edges (like a square wave)requires many (in fact , infinite) sinusoids. Take a look at the data sheet to see the Fourier series fora square wave.(iii)Is incorrect. The Laplace transform is generally useful when the BCs are time varying or there is aforcing term.(iv)Is incorrect. Splines are designed to ensure continuity of the first and second derivatives at all thenodes.Therefore, the solution is B. 3.Which of the following options is the correct inverse Laplace transform of 𝑈𝑈(𝑠𝑠) =𝑠𝑠−1(𝑠𝑠−2)2+1? =1 4. Which of the following graphs best represents the Fourier transform of the function:𝑓𝑓(𝑥𝑥) = 2cos(10𝜋𝜋𝑥𝑥) + 4cos(20𝜋𝜋𝑥𝑥)?AMME2000/AMME29602018QuizSolutions,Page2 of6   • • • 