Question

4. [16 marks] The Error Function function is defined as (a) Starting with the series for e", find the series representation of Erf(x). (b) Use a computer package (eg Matlab, Octave, Excel etc) to plot the series approximation for Erf(x) (using the first four non-zero terms) for x e (0,2]. Plot Erf(x) over the same range on the same axis and comment. (c) Estimate Erf(1.0) using the first 4 non-zero terms in the series and compare with the approx- imation Erf (1.0) 0.842700792950

Answer 1

clc
clear all
close all
Erf=@(x) 2/sqrt(pi)*integral(@(u) exp(-u.^2),0,x);
x=0:0.05:2;
E=[];
Ea=erf(x);
for i=1:length(x)
E(i)=Erf(x(i));
end
plot(x,E,x,Ea,'--g');
legend('Approximation','Exact erf(x)');
fprintf('Approximation of Erf(1) is %f\n',Erf(1));

MATLAB R2018a ② ▼| rch Documentation Log In EDITOR Find Files Compare ▼ Print Run Section New Open Save Advance Runa Figure 1 Find Indent Advance Eile Edit Yiew Insert Tools Desktop Window Help C: Users PRADEEP KALRA 、Documents MATLAB Editor- Current Folder Name- saveee.m xlbisectionmethodbypradeep.m Х| newtonra A 2clear all close all mathlab E ーApproximation -Exact erf(x 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 4-Erf- (x) 2/sqrt (pi) integral ( (u) exp (-u. 5-x 0:0.05:2: 6-E-11 7-Ea erf (x) 8- 무 for i-l: length (x) in New folder a1.m a4.m a5.m A1.dat A1.mat A2.dat A3.dat 4.dat E (1) =Erf (X (1) ) ; 10-end 12legend ("Approximation, "Exact erf (x)) 13- fprint f('Approximation of Erf (1) 13 %f\n' Command Window New to MATLAB? See resources for Getting Started Details Approximation of Erf (l) is 0.842701 Name ▲ Value 41 double x41 double 0 0.2 0.4 0.6 08 1 1.2 1.4 1.6 1.82 Erf 2sqrtpi"integ.. 41 41 double Ln 13 Col 51 script ENG 1:59 PM US 05 06/19 O Type here to search