A set of two or more equations in two or more variables that includes at least one nonlinear equation is referred to as a system of nonlinear equations. Remember that an equation can be linear if it has the expression Ax + By + C = 0. Any equation that is not capable of being expressed in this way is nonlinear. We will utilize the same substitution strategy for nonlinear systems as we did for linear systems. The first equation is solved for a single variable, and the answer is then added to the second equation to solve for a second variable, and so on. However, there are other scenarios that might happen.

The point of intersection of the two lines served as the system's solution while linear equations were being solved. Systems of nonlinear equations can have graphs that are circles, parabolas, or hyperbolas, as well as a number of locations where their lines cross, resulting in a number of solutions. Once the graphs have been identified, consider the many ways the graphs could cross and the potential number of solutions.

In this “Solution of Nonlinear Equations - Numerical Methods” you will learn about the following topics:

1. Review of calculus and Taylor's theorem
2. Errors in numerical calculations
3. Bracketing methods for locating a root
4. Initial approximation and convergence criteria
5. Trial and error method
6. Bisection method
7. Newton's method
8. False position method
9. Secant method and their convergence
10. Fixed point iteration and its convergence

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This article Solution of Nonlinear Equations - Numerical Methods is contributed by Namrata Chaudhary, a student of Lumbini Engineering College (LEC).

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