Solving Non-linear equation (Linearization) - حل أنظمة المعادلات غير الخطية بإستخدام الماتلاب

تعديل :
الخطوة الثانية 2 factorization
Solving Non-linear equation (Linearization)
حل نظام المعادلات غير الخطية بإستخدام الماتلاب
Linearization : is an operation to solve Non-linear equation using arithmetic methods that depend on iteration .
The main theory to doing that is Taylor’s Series
Taylor Series
Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.
Taylor series for function f(x)given as
Taylor Series
In Linearizationion we need just the first item in series which contain the first derivative of the function .
In multi variable functions we will use partial derivatives .
Linearizition algorithm
Derive the functions
Generalization
Find initial values of the variables and set current initials
Form Design matrix using initials
Form constants matrix using initials
Calculate partials using least squares
Adding results to the initial values
Go to 4
Continue until get very small values for partials
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