Question

Consider the following partial differential equation: ?c/?t = D ?²c/?x² - U ?c/?x - kc As c is a function such that c = c(x, t); D, U and k are real constants. 0 ? x ? 10 Initial condition ? c(x, 0) = 0 ?t=0.005 s, ?x=0.1 m, D = 1, U = 5, k = 0.5 Write a MATLAB code to solve the given boundary value problem numerically using an explicit finite difference method, for the boundary conditions given below: a- Constant boundary conditions ? c(0, t) = 100 and c(10, t) = 0 Plot solutions at t = 0.25, 0.5, 0.75 and 1 s. b- Derivative boundary condition at the first grid point: ?c/?x|_{x=0} = 1 c(10, t) = 0 Plot solutions at t = 2, 4, 6 and 8 s. c- Derivative boundary condition at the last grid point: c(0, t) = 100 ?c/?x|_{x=10} = 1 Plot solutions at t = 0.5, 1, 1.5 and 2 s. Use first-order central differencing for the derivative boundary conditions.

          Consider the following partial differential equation:
?c/?t = D ?²c/?x² - U ?c/?x - kc
As c is a function such that c = c(x, t); D, U and k are real constants.
0 ? x ? 10
Initial condition ? c(x, 0) = 0
?t=0.005 s, ?x=0.1 m, D = 1, U = 5, k = 0.5

Write a MATLAB code to solve the given boundary value problem numerically using an explicit finite difference method, for the boundary conditions given below:

a- Constant boundary conditions ? c(0, t) = 100 and c(10, t) = 0
Plot solutions at t = 0.25, 0.5, 0.75 and 1 s.

b- Derivative boundary condition at the first grid point:
?c/?x|_{x=0} = 1
c(10, t) = 0
Plot solutions at t = 2, 4, 6 and 8 s.

c- Derivative boundary condition at the last grid point:
c(0, t) = 100
?c/?x|_{x=10} = 1
Plot solutions at t = 0.5, 1, 1.5 and 2 s.

Use first-order central differencing for the derivative boundary conditions.

Consider the following partial differential equation:
?c/?t = D ?²c/?x² - U ?c/?x - kc
As c is a function such that c = c(x, t); D, U and k are real constants.
0 ? x ? 10
Initial condition ? c(x, 0) = 0
?t=0.005 s, ?x=0.1 m, D = 1, U = 5, k = 0.5

Write a MATLAB code to solve the given boundary value problem numerically using an explicit finite difference method, for the boundary conditions given below:

a- Constant boundary conditions ? c(0, t) = 100 and c(10, t) = 0
Plot solutions at t = 0.25, 0.5, 0.75 and 1 s.

b- Derivative boundary condition at the first grid point:
?c/?x|x=0 = 1
c(10, t) = 0
Plot solutions at t = 2, 4, 6 and 8 s.

c- Derivative boundary condition at the last grid point:
c(0, t) = 100
?c/?x|x=10 = 1
Plot solutions at t = 0.5, 1, 1.5 and 2 s.

Use first-order central differencing for the derivative boundary conditions.

Added by Mark R.

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