Having watched the presentation, we will go through the following exercise: 2.1 Stating the Problem Summarize in a sentence or two what you are trying to achieve using Richardson extrapolation together with various approximations of the derivative. Your summary here. 2.2 Determining the Formal Parameters We are approximating a 1st- or 2nd- derivative using a centred divided-difference approximation and using Richardson extrapolation to improve on the result. The required parameters are: Table 2.1b.i Real-valued constants given in the mathematical problem. Given Description Values Your description here ... x Your description here ... h List any given functions that will be required for Richardson extrapolation. For each function, fill in a row of Table 2.1b.ii. Recall that in Matlab, when a function is passed as an argument, you must pass it with which creates a function handle. @f Table 2.1b.ii Functions given in the mathematical problem. Given Arguments Description Functions The function takes a function and two real-values, and D u, x, h D u x and ... . h, It approximates ... . The function is a real-valued function of a real variable... u x u Each numerical method will have parameters that describe how the method will be used. In this case, the numerical method requires a maximum bound on the number of iterations, and a tolerance after which we will halt, Give a description of abs. Nmax these parameters in Table 2.1b.iii. Table 2.1b.iii Parameters that control the numerical solver. Method Description Parameters
Having watched the presentation, we will go through the following exercise: 2.1 Stating the Problem Summarize in a sentence or two what you are trying to achieve using Richardson extrapolation together with various approximations of the derivative. Your summary here. 2.2 Determining the Formal Parameters We are approximating a 1st- or 2nd- derivative using a centred divided-difference approximation and using Richardson extrapolation to improve on the result. The required parameters are: Table 2.1b.i Real-valued constants given in the mathematical problem. Given Values Description x Your description here ... h Your description here ... List any given functions that will be required for Richardson extrapolation. For each function, fill in a row of Table 2.1b.ii. Recall that in Matlab, when a function is passed as an argument, you must pass it with @f which creates a function handle. Table 2.1b.ii Functions given in the mathematical problem. Given Functions Arguments Description D u, x, h The function D takes a function u and two real-values, x and h, and ... . It approximates ... . u x The function u is a real-valued function of a real variable... Each numerical method will have parameters that describe how the method will be used. In this case, the numerical method requires a maximum bound on the number of iterations, Nmax and a tolerance after which we will halt, abs. Give a description of these parameters in Table 2.1b.iii. Table 2.1b.iii Parameters that control the numerical solver. Method Parameters Description
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