Equations

# Nonlinear Equation System Roots

Solution of nonlinear systems of equations with many unknowns. Finding the roots of complex numbers, if any.

 Variable Number : 1 2 3
 Equations\begin{equation*}\mathcal{F}\left(\mathcal{X}\right)=0\end{equation*} $$f_{1}\left ( x,y\right)=$$ $$f_{2}\left ( x,y\right)=$$
 Iteration Initial Vector $$x_{0}=$$ + $$i$$ $$y_{0}=$$ + $$i$$
 Max. Iter. Number Max. Error

$$\begin{array}{lll|lll} x^a & \Rightarrow & x.\mathrm{pow(a)} \\\sin\, x & \Rightarrow & x.\mathrm{sin} & \arcsin\,x & \Rightarrow & x.\mathrm{asin} \\\cos\,x & \Rightarrow &x.\mathrm{cos} & \arccos\,x & \Rightarrow & x.\mathrm{acos} \\\tan\,x & \Rightarrow & x.\mathrm{tan} & \arctan\,x & \Rightarrow & x.\mathrm{atan} \\\ln\,x & \Rightarrow & x.\mathrm{ln} & e^x & \Rightarrow & x.\mathrm{exp} \\x^2 & \Rightarrow & x.\mathrm{sqr} & \sqrt{x} & \Rightarrow & x.\mathrm{sqrt} \\ x^3 & \Rightarrow & x.\mathrm{cubic} & \sqrt[3]{x} & \Rightarrow & x.\mathrm{cbrt} \\ \\\pi \textrm{ sayısı}& \Rightarrow & \mathrm{pi} & e \textrm{ sayısı} & \Rightarrow & \mathrm{esay} \\\end{array}$$

Use a period (.) as a decimal separator.

Example: Let's solve the following system of equations.
$$\begin{matrix} x^2+y^{2.5}=4 \\ y+e^{x}=1 \end{matrix}$$

$$\begin{matrix} f_1(x,y)=x^2+y^{2.5}-4=0 \\ f_2(x,y)=y+e^{x}-1=0 \end{matrix}$$
takes the form of the equation. From these equations;
$$f_1(x,y)$$ : x.sqr+y.pow(2.5)-4 ,
$$f_2(x,y)$$ : y+x.exp-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.
 Equation Solution Nonlinear Equation System Roots Linear Equation System Solution Cubic Equation Solution Quartic Equation Solution Quintic Equation Solution Sextic Equation Solution Differential Equations

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