Topic
FTCS scheme
About: FTCS scheme is a research topic. Over the lifetime, 1879 publications have been published within this topic receiving 35255 citations. The topic is also known as: Forward Time Centered Space & Forward Time Centered Space method.
Papers published on a yearly basis
1 / 2
Papers
1 Jan 1947
TL;DR: In this paper, the authors present methods of evaluating numerical solutions of the non-linear partial differential equation to the boundary conditions A, k, q are known constants, where q is the rate of heat generation.
Abstract: This paper is concerned with methods of evaluating numerical solutions of the non-linear partial differential equationwheresubject to the boundary conditionsA, k, q are known constants.Equation (1) is of the type which arises in problems of heat flow when there is an internal generation of heat within the medium; if the heat is due to a chemical reaction proceeding at each point at a rate depending upon the local temperature, the rate of heat generation is often defined by an equation such as (2).
3,445 citations
854 citations
684 citations
1 Jun 1994
TL;DR: A family of five-stage fourth-order Runge-Kutta schemes is derived; these schemes required only two storage locations and are considerably more efficient and accurate than existing third-order low-storage schemes.
Abstract: A family of five-stage fourth-order Runge-Kutta schemes is derived; these schemes required only two storage locations. A particular scheme is identified that has desirable efficiency characteristics for hyperbolic and parabolic initial (boundary) value problems. This scheme is competitive with the classical fourth-order method (high-storage) and is considerably more efficient and accurate than existing third-order low-storage schemes.
616 citations
TL;DR: This paper combines the forward time centered space (FTCS) method with the Grunwald--Letnikov discretization of the Riemann--Liouville derivative to obtain an explicit FTCS scheme for solving the fractional diffusion equation.
Abstract: A numerical method for solving the fractional diffusion equation, which could also be easily extended to other fractional partial differential equations, is considered. In this paper we combine the forward time centered space (FTCS) method, well known for the numerical integration of ordinary diffusion equations, with the Grunwald--Letnikov discretization of the Riemann--Liouville derivative to obtain an explicit FTCS scheme for solving the fractional diffusion equation. The stability analysis of this scheme is carried out by means of a powerful and simple new procedure close to the well-known von Neumann method for nonfractional partial differential equations. The analytical stability bounds are in excellent agreement with numerical test. A comparison between exact analytical solutions and numerical predictions is made.
615 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 7 |
| 2024 | 5 |
| 2023 | 14 |
| 2022 | 23 |
| 2021 | 15 |
| 2020 | 6 |