Could you answer the following question with 1-2 sentences. You can use Numerical Methods for Engineers (7th Ed) by Stevan C. Chapra if needed.

 

1) For fitting a cubic spline to a set of n+1 data points what is:

i) The number of interior knots?

ii) The minimum number of equations in the system of equation that must be solved?

iii) The special matrix form of this system of equations?

 

2) Which Runge-Kutta (RK) numerical methods for solving differential equations can be applied in an iterative fashion at each step? Explain Why?

 

3) What is the main characteristic of data used to determine when to use interpolation vs. regression?

 

4) For the following methods for solving differential equations of the form dy/dx = f(x,y): a) Midpoint, b) Euler's, c) Iterative Heun's (j iterations). List the methods in ascending order of the number (n) of function (f) evaluations required to estimate the final value of y at each step. AND state what the value of n is for each method?

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