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What is the difference between nonlinear and linear equations?
== Linear equations are those that use only linear functions and operations. Examples of linearity: differentiation, integration, addition, subtraction, logarithms, multiplication or division by a constant, etc. Examples of non-linearity: trigonometric functions (sin, cos, tan, etc.), multiplication or division by variables.
What is numerical solutions of nonlinear equations?
Linear equations, if they have a solution, can be solved analytically. On the other hand, it may not always be possible to find a solution to nonlinear equations. This is where you use various numerical methods (eg Newton-Raphson) to work from one approximate numerical solution to a better solution. This iterative procedure, if properly applied, gives accurate numerical solutions to nonlinear equations. But as mentioned above, they are not arrived at analytically.
How are linear equations and functions alike?
They are not. A vertical line is not a function so all linear equations are not functions. And all functions are not linear equations.
How are functions and linear equations similar?
Linear equations are a small minority of functions.
How are functions like linear equations?
Most functions are not like linear equations.
Examples of nonlinear equations?
y=x2 and y=lnx are two examples of nonlinear equations.
What has the author C V Pao written?
C. V. Pao has written: 'Nonlinear parabolic and elliptic equations' -- subject(s): Differential equations, Nonlinear, Nonlinear Differential equations
What has the author Elemer E Rosinger written?
Elemer E. Rosinger has written: 'Generalized solutions of nonlinear partial differential equations' -- subject(s): Differential equations, Nonlinear, Differential equations, Partial, Nonlinear Differential equations, Numerical solutions, Partial Differential equations 'Distributions and nonlinear partial differential equations' -- subject(s): Differential equations, Partial, Partial Differential equations, Theory of distributions (Functional analysis)
What has the author Enzo Mitidieri written?
Enzo Mitidieri has written: 'Apriori estimates and blow-up of solutions to nonlinear partial differential equations and inequalities' -- subject(s): Differential equations, Nonlinear, Differential equations, Partial, Inequalities (Mathematics), Nonlinear Differential equations, Partial Differential equations
What has the author R Grimshaw written?
R. Grimshaw has written: 'Nonlinear ordinary differential equations' -- subject(s): Nonlinear Differential equations
What has the author S Zheng written?
S. Zheng has written: 'Nonlinear parabolic equations and hyperbolic-parabolic coupled systems' -- subject(s): Hyperbolic Differential equations, Nonlinear Differential equations, Parabolic Differential equations
What has the author P L Sachdev written?
P. L. Sachdev has written: 'A compendium on nonlinear ordinary differential equations' -- subject(s): Differential equations 'Large time asymptotics for solutions of nonlinear partial differential equations' -- subject(s): Nonlinear Differential equations, Asymptotic theory, Nichtlineare partielle Differentialgleichung
What has the author J L Blue written?
J. L Blue has written: 'B2DE' -- subject(s): Computer software, Differential equations, Elliptic, Differential equations, Nonlinear, Differential equations, Partial, Elliptic Differential equations, Nonlinear Differential equations, Partial Differential equations
How many solutions does the nonlinear system of equations graphed below have?
2
What has the author Laurent Veron written?
Laurent Veron has written: 'Singularities of solutions of second order quasilinear equations' -- subject(s): Differential equations, Elliptic, Differential equations, Nonlinear, Differential equations, Parabolic, Elliptic Differential equations, Nonlinear Differential equations, Numerical solutions, Parabolic Differential equations, Singularities (Mathematics)
What has the author Jeffrey S Scroggs written?
Jeffrey S. Scroggs has written: 'An iterative method for systems of nonlinear hyperbolic equations' -- subject(s): Algorithms, Hyperbolic Differential equations, Iterative solution, Nonlinear equations, Parallel processing (Computers)
Are linear equations and functions different?
All linear equations are functions but not all functions are linear equations.
