Construct Green's function for the differential equation
under the conditions that y(0) is bounded and .
Based on the image provided, here is the transcription of the mathematical problems:
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Solve the heat conduction equation in the region
with the initial and boundary conditions
using Crank-Nicolson method with
and
upto two time steps.
Based on the third image provided, here is the transcription of the remaining mathematical problems:
Find an approximate value of y(1.0) for the initial value problem
y = x - 2y, y(0) = 1
using Milne-Simpson’s method
with the step length . Calculate the starting value using Runge-Kutta fourth order method with the same h.
Using the transformation find the solution of the equation
in terms of Bessel's functions.
Solve the wave equation with the initial and boundary conditions
.
with , using the explicit method upto four time levels.
If the Fourier cosine transform of f(x) is , then show that
) Using fourth order Taylor series method with , solve the initial value problem
upto .
Construct Green's function for the differential equation
under the conditions that y(0) is bounded and .
Based on the image provided, here is the transcription of the mathematical problems: