Nonlinear Equation System Roots
Solution of non-linear equation systems with many unknowns by Newton-Raphson iteration method.
Click to find the complex roots as well.
Functions to be used in the equation:\(\begin{array}{lll|lll} x^a & \Rightarrow & \mathrm{pow(x,a)} \\\sin\, x & \Rightarrow & \mathrm{sin(x)} &\cos\,x & \Rightarrow & \mathrm{cos(x)} \\\tan\,x & \Rightarrow &\mathrm{tan(x)} &\ln\,x & \Rightarrow & \mathrm{log(x)} \\e^x & \Rightarrow & \mathrm{exp(x)} &\left|x\right| & \Rightarrow & \mathrm{abs(x)} \\\arcsin\,x & \Rightarrow & \mathrm{asin(x)} &\arccos\,x & \Rightarrow & \mathrm{acos(x)} \\\arctan\,x & \Rightarrow & \mathrm{atan(x)} &\sqrt{x} & \Rightarrow & \mathrm{sqrt(x)} \\ \\\pi & \Rightarrow & \mathrm{pi} &e \textrm{ sayısı} & \Rightarrow & \mathrm{esay} \\\ln\,2 & \Rightarrow &\mathrm{LN2} & \ln\,10 & \Rightarrow & \mathrm{LN10} \\\log_{2}\,e & \Rightarrow & \mathrm{Log2e} & \log_{10}\,e & \Rightarrow & \mathrm{Log10e} \end{array}\)
Use a period (.) as a decimal separator.
Example: Let's solve the following system of equations.
\( \begin{matrix} x^2+y^2=4 \\ y+e^x=1 \end{matrix}\)
\( \begin{matrix} f_1(x,y)=x^2+y^2-4=0 \\ f_2(x,y)=y+e^x-1=0 \end{matrix}\)
takes the form of the equation. From these equations;
\(f_1(x,y)\) : pow(x,2)+pow(y,2)-4 ,
\(f_2(x,y)\) : y+pow(esay,x)-1
is written. As the start of iteration, typing \(x_0=1.0\), \(y_0=-1.7\) for example and clicking "Calculate" will give us the result vector. Some equations can have more than one solution. These solutions can be reached with different initial values.