Iteration to convergance

Hi there, I have an equation in which the variable I'm solving for is in the equation. I'm working on solving my equation by using iterations until the variable converges. I have a painfully basic method of doing this but I'm looking to program this with something like a "for loop". Unfortunately I have Noo Idea how to. Any help would be greatly appreciated.

Thanks,

Ethan

Ps. this is an equation to determine heat flow.

clear all
close all
%Constants

lambdaE=2.8;  %Effecitve Thermal Conductivity

p=2.7; %Density of Fluid and Sediment

c=4.2;  %Heat Capacity of Fluid and Sediment

Ke=[lambdaE/(p*c)];  %Effective Thermal Diffusivity

f=2;  %Frequency

P=(1/f);  %Period

v=10; %Fluid Velocity (initial)

deltaPhi = 0.004;  %Phase shift between shallow and deep points [Measured in the Lab]

Ar = 0.1; %Amp ratio of shallow and deep points[Measured in the Lab]

deltaZ=.2;  %Distance between shallow and deep points

alpha=sqrt(v^4+(8*pi*Ke/P)^2);

Amp Method

%Ar=exp((deltaZ/(2*Ke))*(v-sqrt((alpha + v^2)/2)))

v1=(((2*Ke)/deltaZ)*log(Ar))+ sqrt((alpha+v^2)/2)

v2=(((2*Ke)/deltaZ)*log(Ar))+ sqrt((alpha+v1^2)/2)

v3=(((2*Ke)/deltaZ)*log(Ar))+ sqrt((alpha+v2^2)/2)

v4=(((2*Ke)/deltaZ)*log(Ar))+ sqrt((alpha+v3^2)/2)

v5=(((2*Ke)/deltaZ)*log(Ar))+ sqrt((alpha+v4^2)/2)

v6=(((2*Ke)/deltaZ)*log(Ar))+ sqrt((alpha+v5^2)/2)

v7=(((2*Ke)/deltaZ)*log(Ar))+ sqrt((alpha+v6^2)/2)

v8=(((2*Ke)/deltaZ)*log(Ar))+ sqrt((alpha+v7^2)/2)

v9=(((2*Ke)/deltaZ)*log(Ar))+ sqrt((alpha+v8^2)/2)

v10=(((2*Ke)/deltaZ)*log(Ar))+ sqrt((alpha+v9^2)/2)

v11=(((2*Ke)/deltaZ)*log(Ar))+ sqrt((alpha+v10^2)/2)

v12=(((2*Ke)/deltaZ)*log(Ar))+ sqrt((alpha+v11^2)/2)

v13=(((2*Ke)/deltaZ)*log(Ar))+ sqrt((alpha+v12^2)/2)

v14=(((2*Ke)/deltaZ)*log(Ar))+ sqrt((alpha+v13^2)/2)

v15=(((2*Ke)/deltaZ)*log(Ar))+ sqrt((alpha+v14^2)/2)

v16=(((2*Ke)/deltaZ)*log(Ar))+ sqrt((alpha+v15^2)/2)

v17=(((2*Ke)/deltaZ)*log(Ar))+ sqrt((alpha+v16^2)/2)

v18=(((2*Ke)/deltaZ)*log(Ar))+ sqrt((alpha+v17^2)/2)

v19=(((2*Ke)/deltaZ)*log(Ar))+ sqrt((alpha+v18^2)/2)

v20=(((2*Ke)/deltaZ)*log(Ar))+ sqrt((alpha+v19^2)/2)

v21=(((2*Ke)/deltaZ)*log(Ar))+ sqrt((alpha+v20^2)/2)

v22=(((2*Ke)/deltaZ)*log(Ar))+ sqrt((alpha+v21^2)/2)

v23=(((2*Ke)/deltaZ)*log(Ar))+ sqrt((alpha+v22^2)/2)

v24=(((2*Ke)/deltaZ)*log(Ar))+ sqrt((alpha+v23^2)/2)

v25=(((2*Ke)/deltaZ)*log(Ar))+ sqrt((alpha+v24^2)/2)

Answer 1

[Walter Roberson]

I already showed the method in response to your previous question on this topic, http://www.mathworks.com/matlabcentral/answers/15351-iteration-to-convergence