New stable, explicit, shifted-hopscotch algorithms for the heat equation
Our goal was to find more effective numerical algorithms to solve the heat or diffusion
equation. We created new five-stage algorithms by shifting the time of the odd cells in the …
equation. We created new five-stage algorithms by shifting the time of the odd cells in the …
Stable, explicit, leapfrog-hopscotch algorithms for the diffusion equation
In this paper, we construct novel numerical algorithms to solve the heat or diffusion equation.
We start with 105 different leapfrog-hopscotch algorithm combinations and narrow this …
We start with 105 different leapfrog-hopscotch algorithm combinations and narrow this …
Advanced analytic self-similar solutions of regular and irregular diffusion equations
We study the diffusion equation with an appropriate change of variables. This equation is, in
general, a partial differential equation (PDE). With the self-similar and related Ansatz, we …
general, a partial differential equation (PDE). With the self-similar and related Ansatz, we …
Solution of the 1D KPZ equation by explicit methods
The Kardar–Parisi-Zhang (KPZ) equation is examined using the recently published leapfrog–
hopscotch (LH) method as well as the most standard forward time centered space (FTCS) …
hopscotch (LH) method as well as the most standard forward time centered space (FTCS) …
Division by zero calculus and differential equations
S Pinelas, S Saitoh - International Conference on Differential & Difference …, 2017 - Springer
Division by Zero Calculus and Differential Equations | SpringerLink Skip to main content
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A new stable, explicit, and generic third‐order method for simulating conductive heat transfer
In this paper we introduce a new type of explicit numerical algorithm to solve the spatially
discretized linear heat or diffusion equation. After discretizing the space variables as in …
discretized linear heat or diffusion equation. After discretizing the space variables as in …
[PDF][PDF] CONSTRUCTION AND INVESTIGATION OF NEW NUMERICAL ALGORITHMS FOR THE HEAT EQUATION Part 1
In this paper-series, we use two known, but non-conventional algorithms, the UPFD and the
odd-even hopscotch method, to construct new schemes for the numerical solution of the …
odd-even hopscotch method, to construct new schemes for the numerical solution of the …
[PDF][PDF] Review on relationship between the universality class of the Kardar-Parisi-Zhang equation and the ballistic deposition model
We have analysed the research findings on the universality class and discussed the
connection between the Kardar-Parisi-Zhang (KPZ) universality class and the ballistic …
connection between the Kardar-Parisi-Zhang (KPZ) universality class and the ballistic …
Numerical solutions of the Kardar-Parisi-Zhang interface growing equation with different noise terms
Abstract The one-dimensional Kardar-Parisi-Zhang dynamic interface growth equation with
Gaussian noise and without noise term is analyzed in various initial conditions and its …
Gaussian noise and without noise term is analyzed in various initial conditions and its …
Even and odd self-similar solutions of the diffusion equation for infinite horizon
In the description of transport phenomena, diffusion represents an important aspect. In
certain cases, the diffusion may appear together with convection. In this paper, we study the …
certain cases, the diffusion may appear together with convection. In this paper, we study the …