Numerical Integration
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ECE 5431 homework #2,
Part (a): Numerical Integration (30 points)
- Approximate the area under the curve ()= 4 ^2 over 0 << 1 by the trapezoidal rule with a) h=0. b) h=0. Compare your results from above with the exact value.
- Evaluate the integral
^2 ( 2 )
0 using Gaussian quadrature^
- Compute 1 0 using Simpsons rule with h=0.^
For each problem provide
- Typed description of the general integration rule
- Explanation of the steps as you apply the integration rule.
- Results
Part (b):Method of Moments (70 points)
In this assignment you are asked to compute the induced current distribution along a wire scatterer. Consider a straight wire of length L= /2 and radius a, such that a << and a << L, where is wavelength. Let a plane wave be the excitation source.
Expand the unknown current using piecewise constant (pulse) basis functions as given in Equation (5.144a) of the Sadiku text.
Use point-matching for testing (weighting functions) as described in Equation (4.46).
You should solve Pocklingtons equation in order to determine the currents along the wire.
Please turn in the following items: (1) A typed report describing your application of the method of moments to Pocklingtons equation, showing the analytical forms of the matrix elements as well as the right-hand-side source terms.
(3) Plots of solved currents along the wire length.
(4) Your program (m-file) with pseudocode.
For the solution of the system of equations it is acceptable to utilize built-in mat lab functions, or equivalent. In other words, you do not have to write code to perform the system of equations solution.