I'm trying to determine stability criteria for a particular case of nonlinear diffusion $$ \frac{\partial u}{\partial t} = \frac{\partial }{\partial x}\left(g(u)\frac{\partial u}{\partial x}\right), $$ using finite differences. For linear diffusion Von Neumann Stability analysis can be used to get the result $$ \nu \frac{\Delta t}{(\Delta x)^2} \leq \frac{1}{2}, $$ but I'm not sure where to start for nonlinear diffusion since the same technique does not appear to work. Any references of where to look would be appreciated!
2026-03-27 02:50:43.1774579843
How to determine stability of nonlinear diffusion equation using explicit finite difference scheme?
287 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in PARTIAL-DIFFERENTIAL-EQUATIONS
- PDE Separation of Variables Generality
- Partial Derivative vs Total Derivative: Function depending Implicitly and Explicitly on Variable
- Transition from theory of PDEs to applied analysis and industrial problems and models with PDEs
- Harmonic Functions are Analytic Evan’s Proof
- If $A$ generates the $C_0$-semigroup $\{T_t;t\ge0\}$, then $Au=f \Rightarrow u=-\int_0^\infty T_t f dt$?
- Regular surfaces with boundary and $C^1$ domains
- How might we express a second order PDE as a system of first order PDE's?
- Inhomogeneous biharmonic equation on $\mathbb{R}^d$
- PDE: Determine the region above the $x$-axis for which there is a classical solution.
- Division in differential equations when the dividing function is equal to $0$
Related Questions in NUMERICAL-METHODS
- The Runge-Kutta method for a system of equations
- How to solve the exponential equation $e^{a+bx}+e^{c+dx}=1$?
- Is the calculated solution, if it exists, unique?
- Modified conjugate gradient method to minimise quadratic functional restricted to positive solutions
- Minimum of the 2-norm
- Is method of exhaustion the same as numerical integration?
- Prove that Newton's Method is invariant under invertible linear transformations
- Initial Value Problem into Euler and Runge-Kutta scheme
- What are the possible ways to write an equation in $x=\phi(x)$ form for Iteration method?
- Numerical solution for a two dimensional third order nonlinear differential equation
Related Questions in HEAT-EQUATION
- Solving the heat equation with robin boundary conditions
- Duhamel's principle for heat equation.
- Computing an inverse Fourier Transform / Solving the free particle Schrödinger equation with a gaussian wave packet as initial condition
- Bound on the derivatives of heat kernel.
- Imposing a condition that is not boundary or initial in the 1D heat equation
- 1-D Heat Equation, bounding difference in $\alpha$ given surface temperature
- Heat equation for a cylinder in cylindrical coordinates
- Heat Equation in Cylindrical Coordinates: Sinularity at r = 0 & Neumann Boundary Conditions
- Applying second-order differential operator vs applying first-order differential operator twice?
- Physical Interpretation of Steady State or Equilibrium Temperature.
Related Questions in FINITE-DIFFERENCES
- 4-point-like central finite difference for second partial derivatives
- Numerical method for fourth order PDE.
- Finite difference approximation of $u''(x)+u(x)=0, u(0)=1, u(\pi)=-1$
- Numerically compute Laplacian of a scalar field in a non-orthogonal grid
- write second order difference as a convolution operator
- Do the second differences of the fifth powers count the sphere packing of a polyhedron?
- Discretization for $\partial_tu = \partial_x[g\times\partial_xu]$
- Discretization of 4th order ODE
- Trying to use Matlab to find Numerical Solution to $u''(x)+e^{u(x)}=0, u(0)=0, u(1)=0$ - Newton's method
- Finite difference: problem on edge of Dirichlet and Neumann boundary
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?