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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.
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Do there exists solution of all types of differential equations?
No, analytical solutions do not always exist. That is to say, the answer need not be a function. However, it is possible to find numerical solutions.
Can nonlinear equations also be functions?
yes
What is a numerical solution of a partial differential equation?
Some partial differential equations do not have analytical solutions. These can only be solved numerically.
What is the theory of finite differential method?
Finite Differential Methods (FDM) are numerical methods for approximating the solutions to differential equations using finite difference equations to approximate derivatives.
How do you answer equations?
The answers to equations are their solutions
What has the author J C P Bus written?
J. C. P. Bus has written: 'Numerical solution of systems of nonlinear equations' -- subject(s): Nonlinear Differential equations, Numerical solutions
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J.E Dennis has written: 'Numerical methods for unconstrained optimization and nonlinear equations' -- subject(s): Numerical solutions, 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 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 Eduard Reithmeier written?
Eduard Reithmeier has written: 'Periodic solutions of nonlinear dynamical systems' -- subject(s): Differentiable dynamical systems, Nonlinear Differential equations, Numerical solutions
What has the author P C den Heijer written?
P. C. den Heijer has written: 'The numerical solution of nonlinear operator equations by imbedding methods' -- subject(s): Convergence, Iterative methods (Mathematics), Nonlinear Operator equations, Numerical solutions
What has the author Lynn Taylor Winter written?
Lynn Taylor Winter has written: 'Computer techniques yielding automatic and rigorous solutions to linear and nonlinear integral equations' -- subject(s): Numerical solutions, Integral equations
What has the author Killion Noh written?
Killion Noh has written: 'A numerical solution of the matrix Riccati equations' -- subject(s): Nonlinear Differential equations, Numerical solutions, Matrices 'Computational techniques for input-output econometric models' -- subject(s): Input-output 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 Alain Haraux written?
Alain Haraux has written: 'Semi-linear hyperbolic problems in bounded domains' -- subject(s): Boundary value problems, Nonlinear Evolution equations 'Nonlinear vibrations and the wave equation' -- subject(s): Numerical solutions, Vibration, Wave equation, Nonlinear systems
How many solutions does the nonlinear system of equations graphed below have?
2
What has the author J C Butcher written?
J. C. Butcher has written: 'Numerical Methods for Ordinary Differential Equations' -- subject(s): Differential equations, Mathematics, Nonfiction, Numerical solutions, OverDrive 'The numerical analysis of ordinary differential equations' -- subject(s): Differential equations, Numerical solutions, Runge-Kutta formulas
