Solution of nonlinear (nonlinear, multivariable) equation systems using the Newton–Raphson iteration method.
Since the calculation is implemented in JavaScript, the usable functions are the JavaScript Math
functions listed below.
Functions that can be used inside the equations:
\(\begin{array}{lll|lll} x^a & \Rightarrow & \mathrm{pow(x,a)} \\\sin\, x & \Rightarrow & \mathrm{sin(x)} &\cos\,x & \Rightarrow & \mathrm{cos(x)} \\\tan\,x & \Rightarrow &\mathrm{tan(x)} &\ln\,x & \Rightarrow & \mathrm{log(x)} \\e^x & \Rightarrow & \mathrm{exp(x)} &\left|x\right| & \Rightarrow & \mathrm{abs(x)} \\\arcsin\,x & \Rightarrow & \mathrm{asin(x)} &\arccos\,x & \Rightarrow & \mathrm{acos(x)} \\\arctan\,x & \Rightarrow & \mathrm{atan(x)} &\sqrt{x} & \Rightarrow & \mathrm{sqrt(x)} \\ \\\pi & \Rightarrow & \mathrm{pi} &e \mathrm{ number} & \Rightarrow & \mathrm{esay} \\\ln\,2 & \Rightarrow &\mathrm{LN2} & \ln\,10 & \Rightarrow & \mathrm{LN10} \\\log_{2}\,e & \Rightarrow & \mathrm{Log2e} & \log_{10}\,e & \Rightarrow & \mathrm{Log10e} \end{array}\)
Use a dot (.) as the decimal separator. For example, write 1.0 instead of 1,0.
Example: Let us solve the following system of equations.
\( \begin{matrix}f_1(x,y)= x*x + y*y - 4=0 \end{matrix}\)
\( \begin{matrix} f_2(x,y)=exp(x) + y - 1=0 \end{matrix}\)
For the solution, if we choose the initial values \(x_0=1.0\) and \(y_0=-1.2\), the result is obtained when we click "Calculate".
NOTE: x^2 notation is not supported; use pow(x,2) instead.