A équation non linéaire is an equation that does not form a straight line when graphed on a coordinate plane. This means that the relationship between the variables is not proportional, and the variables may be raised to powers greater than one, multiplied together, or involve other non-linear operations telles que des fonctions exponentielles, logarithmiques ou trigonométriques.
Contrairement aux équations linéaires, qui peuvent être exprimées sous la forme y = mx + b (where m is the slope and b is the y-intercept), non-linear equations can take various forms. Examples include quadratic equations like y = ax² + bx + c, polynomial equations of higher degrees, and equations involving square roots or trigonometric functions.
Les équations non linéaires sont importantes dans de nombreux domaines, notamment physics, engineering, economics, and intelligence artificielle, as they often describe systèmes complexes and relationships. For instance, in apprentissage automatique, non-linear models can capture more intricate patterns in data than linear models can.
Résoudre des équations non linéaires peut être plus difficile que résoudre des équations linéaires, as they may have multiple solutions or none at all. Techniques such as numerical methods, graphical methods, or iterative algorithms are often employed to find solutions to non-linear equations.