Nonstandard finite difference equations for ODEs and 1-D PDEs based on piecewise linearization
From MaRDI portal
Publication:1126587
DOI10.1016/S0096-3003(96)00146-4zbMath0907.65075OpenAlexW2170349946MaRDI QIDQ1126587
C. M. García-López, Juan I. Ramos
Publication date: 4 March 1999
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/s0096-3003(96)00146-4
Nonlinear parabolic equations (35K55) Nonlinear boundary value problems for ordinary differential equations (34B15) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Finite difference and finite volume methods for ordinary differential equations (65L12)
Related Items
Numerical Solution of Singularly Perturbed Non-Linear Two Point Boundary Value Problems by Spline in Compression ⋮ \(\epsilon\)-uniformly convergent nonstandard finite difference methods for singularly perturbed differential difference equations with small delay ⋮ Exponential methods for singularly perturbed ordinary differential-difference equations ⋮ Piecewise-linearized methods for single degree-of-freedom problems ⋮ Piecewise-linearized and linearized \(\vartheta\)-methods for ordinary and partial differential equations. ⋮ A smart nonstandard finite difference scheme for second order nonlinear boundary value problems ⋮ Linearized methods for ordinary differential equations ⋮ On diffusive methods and exponentially fitted techniques ⋮ Intermediate boundary conditions in operator-splitting techniques and linearization methods ⋮ Dynamic properties of the local linearization method for initial value problems. ⋮ Spline techniques for solving singularly-perturbed nonlinear problems on nonuniform grids
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Asymptotic and numerical analysis of singular perturbation problems: A survey
- Numerical study of Fisher's equation by Adomian's method
- Ten ways to generate the Il'in and related schemes
- Piecewise-linearized methods for initial-value problems
- A computational method for solving quasilinear singular perturbation problems
- Multiple scale and singular perturbation methods
- A computational method for solving singular perturbation problems
- Difference methods for solving convection-diffusion equations
- Higher-Order Numerical Solutions Using Cubic Splines
- Construction of a Finite-Difference Scheme that Exactly Conserves Energy for a Mixed Parity Oscillator
- A best finite‐difference scheme for the fisher equation
- Comment on “a second‐order, chaos‐free, explicit method for the numerical solution of a cubic reaction problem in neurophysiology”
- On piecewise-uniform meshes for upwind- and central-difference operators for solving singularly perturbed problems
- Finite-element methods for singularly perturbed high-order elliptic two-point boundary value problems. I: reaction-diffusion-type problems
- Transient analysis by Laplace transform and combined finite and boundary element methods for convective diffusion problem
- Numerical Inversion of Laplace Transforms: An Efficient Improvement to Dubner and Abate's Method
- Finite-element methods for singularly perturbed high-order elliptic two-point boundary value problems. II: convection-diffusion-type problems
- A new pseudospectral method with upwind features
- Adaptive methods of lines for one‐dimensional reaction‐diffusion equations
- A PIECEWISE-LINEARIZED METHOD FOR ORDINARY DIFFERENTIAL EQUATIONS: TWO-POINT BOUNDARY-VALUE PROBLEMS
- RELAXATION METHODS APPLIED TO DETERMINE THE MOTION, IN TWO DIMENSIONS, OF A VISCOUS FLUID PAST A FIXED CYLINDER
