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Chemical Engineering Numerical Methods - Partial Differential Equation Experiments

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Theory

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Procedure

Simulation

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Aim

Theory

Pretest

Procedure

Simulation

Posttest

References

Contributors

Feedback

Differentiation(PDE) - Elliptical equation (Laplace Equation with one end insulated)

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Intermediate

Advanced

u = f(x_j, y_i)\ then \frac{\partial u}{\partial x}

by forward difference is given by

a:

\frac{u_{i+1,j} - u_{i,j}}{h}

Explanation

Explanation

b:

\frac{u_{i-1,j} - u_{i,j}}{h}

Explanation

Explanation

c:

\frac{u_{i,j+1} - u_{i,j}}{h}

Explanation

Explanation

d:

\frac{u_{i,j} - u_{i,j-1}}{h}

Explanation

Explanation

u = f(x_j, y_i)\ then \frac{\partial u}{\partial x}

by backward difference is given by

a:

\frac{u_{i,j} - u_{i,j-1}}{h}

Explanation

Explanation

b:

\frac{u_{i,j+1} - u_{i,j}}{h}

Explanation

Explanation

c:

\frac{u_{i,j+1} - u_{i,j-1}}{2h}

Explanation

Explanation

d:

\frac{u_{i+1,j} - u_{i-1,j}}{2h}

Explanation

Explanation

u = f(x_j, y_i)\ then \frac{\partial^2 u}{\partial x^2}

is given by

a:

\frac{u_{i,j+1} - u_{i,j}}{h}

Explanation

Explanation

b:

\frac{u_{i,j+1} - 2 u_{i,j-1} + u_{i,j-1}}{h^2}

Explanation

Explanation

c:

\frac{u_{i-1,j} - u_{i,j}}{h}

Explanation

Explanation

d:

\frac{u_{i+1,j} - u_{i,j}}{h}

Explanation

Explanation

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