Coincidence and periodic point results in a modular metric space endowed with a graph and applications

2017 ◽  
Vol 26 (1) ◽  
pp. 95-104
Author(s):  
Anantachai Padcharoen ◽  
◽  
Poom Kumam ◽  
Dhananjay Gopal ◽  
◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Periodic Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Partial Differential ◽  
Modular Metric Space ◽  
Modular Metric Spaces ◽  
Contractive Mappings ◽  
Theoretical Results

In this paper, we present some results on the existence of coincidence and periodic point of F-contractive mappings in the framework of modular metric spaces endowed with a graph. We also present an application to partial differential equations in order to support the theoretical results

Exponential global attractors for semigroups in metric spaces with applications to differential equations

2011 ◽  
Vol 31 (6) ◽  
pp. 1641-1667 ◽  
Author(s):  
ALEXANDRE N. CARVALHO ◽  
JAN W. CHOLEWA
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Global Attractor ◽  
Metric Space ◽  
Metric Spaces ◽  
Global Attractors ◽  
Invariant Sets ◽  
Bounded Subset ◽  
Partial Differential ◽  
Unstable Manifolds

AbstractIn this article semigroups in a general metric space V, which have pointwise exponentially attracting local unstable manifolds of compact invariant sets, are considered. We show that under a suitable set of assumptions these semigroups possess strong exponential dissipative properties. In particular, there exists a compact global attractor which exponentially attracts each bounded subset of V. Applications of abstract results to ordinary and partial differential equations are given.

Meir–Keeler type contractive mappings in modular and partial modular metric spaces

2019 ◽  
Vol 13 (05) ◽  
pp. 2050087
Author(s):  
Hasan Hosseinzadeh ◽  
Vahid Parvaneh
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Ordered Metric Spaces ◽  
Modular Metric Space ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Modular Metric Spaces ◽  
Contractive Mappings

In this paper, first, we introduce the class of [Formula: see text]-Meir–Keeler contractive mappings and establish some fixed point results. Next, we introduce the notion of partial modular metric space and establish some fixed point results in this new spaces. As consequences of these results, we deduce some fixed point theorems in modular metric spaces endowed with a graph and in partially ordered metric spaces. Some examples are furnished to demonstrate the validity of the obtained results.

scholarly journals A Crank-Nicolson Difference Scheme for Solving a Type of Variable Coefficient Delay Partial Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Wei Gu ◽  
Peng Wang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Difference Scheme ◽  
Variable Coefficient ◽  
Numerical Test ◽  
Partial Differential ◽  
The Difference ◽  
Delay Partial Differential Equations ◽  
Theoretical Results ◽  
Crank Nicolson

A linearized Crank-Nicolson difference scheme is constructed to solve a type of variable coefficient delay partial differential equations. The difference scheme is proved to be unconditionally stable and convergent, where the convergence order is two in both space and time. A numerical test is provided to illustrate the theoretical results.

scholarly journals An approach to construct higher order time discretisation schemes for time fractional partial differential equations with nonsmooth data

2017 ◽  
Vol 20 (5) ◽  
Author(s):  
Neville J. Ford ◽  
Yubin Yan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Higher Order ◽  
Fractional Partial Differential Equations ◽  
Order Accuracy ◽  
Partial Differential ◽  
Nonsmooth Data ◽  
Standard Time ◽  
Time Discretisation ◽  
Theoretical Results

AbstractIn this paper, we shall review an approach by which we can seek higher order time discretisation schemes for solving time fractional partial differential equations with nonsmooth data. The low regularity of the solutions of time fractional partial differential equations implies standard time discretisation schemes only yield first order accuracy. To obtain higher order time discretisation schemes when the solutions of time fractional partial differential equations have low regularities, one may correct the starting steps of the standard time discretisation schemes to capture the singularities of the solutions. We will consider these corrections of some higher order time discretisation schemes obtained by using Lubich’s fractional multistep methods, L1 scheme and its modification, discontinuous Galerkin methods, etc. Numerical examples are given to show that the theoretical results are consistent with the numerical results.

Sign in / Sign up

Export Citation Format

Share Document