Solution of Nonlinear Equations

What is nonlinear equation?

Nonlinear equation is the mathematical function that has power more than two. It can be depicted as the non-stright line, such as curve or S-shape, depending on the mathematical expresion of a certain case. An example, a \(y = x^2 - 16\) is the simple nonlinear equation. In the real life, especially in science and engineering lifes, we will face with any kind form of nonlinear function from any mathematical problems that should be solved. Back to previous example, what is the solution of \(x\) when \(y = 0\)?. In the analytical way, it is very simple to be solved. By subtituting the \(y = 0\) into the function, we will get the \(x\) by rooting it, where the solution of \(x\) is 4. Imagine that you are a scientist or engineer who asked to solved the solution of a complex nonlinear function from a complex case that can not be solved by analytically. What should you do? Here, the numerical method is approach to solve a solution of nonlinear function. In the following note, you will find the concept to solve a solution of nonlinear equation by using several numerical methods.

Solution of Nonlinear Equations

• Bisection Method
  • Stopping Criteria
  • Algorithm of Bisection Method
  • Case 1
  • Case 2
• False Position
  • Stopping Criteria
  • Algorithm of False Position
  • Case 1
  • Case 2
• Newton Raphson
  • Stopping Criteria
  • Algorithm of Newton-Raphson
  • Case 1
  • Case 2
• Secant Method
  • Stopping Criteria
  • Algorithm of Secant Method
  • Case 1
  • Case 2