Discrete Approximate Solution of Differential Inclusion with Normal Cone and Prox-Regular Set.

Normal Cone ◽

Approximation Property ◽

Knowing That ◽

Nite Element ◽

New Variant ◽

Sweeping Processes

Abstract Our aim is to calculate the discrete approximate solution of di⁄erential inclusion with normal cone and prox-regular set, the question is how to calculate this solution? We use the discrete approximation property of a new variant of nonconvex sweeping processes involving normal cone and a nite element method. Knowing that The majority of mathematicians have proved only the existence and uniqueness of the solution for this type of inclusions, like: Mordukhovich, Thibault, Aubin, Messaoud, ...etc.

Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния ◽

Indignation moving singularity and analytical approximate solution of a nonlinear third-order equations

10.37972/chgpu.2021.1.47.002 ◽

2021 ◽

pp. 16-27

Author(s):

Темирхан Султанович Алероев ◽

Магомедюсуф Владимирович Гасанов

Keyword(s):

Approximate Solution ◽

Singular Point ◽

Numerical Experiment ◽

Nonlinear Differential Equations ◽

Third Order ◽

Proved Theorem ◽

Analytical Approximate Solution ◽

Posterior Estimate

В данной работе представлено исследование рассматриваемого класса нелинейных дифференциальных уравнений с подвижными особыми точками. Учитывая авторскую разработку теоремы существования и единственности решения построена структура аналитического приближенного решения, для которой, в данной работе, было установлено влияние возмущения подвижной особой точки. Представленные теоретические положения подтверждены с помощью численного эксперимента. Для оптимизации априорных оценок применялась апостериорная оценка. This paper presents a study of one class of nonlinear differential equations with movable singular points. On the basis of the previously proved theorem of existence and uniqueness of the solution, the structure of the analytical approximate solution was obtained, for which, in this work, the influence of the perturbation of a moving singular point was established. Results are tested using a numerical experiment. To optimize the prior estimates, the posterior estimate was used.

Hypothesis on the Solvability of Parabolic Equations with nonlocal Condition

Nonlinear Analysis Modelling and Control ◽

10.15388/na.2002.7.1.15204 ◽

2002 ◽

Vol 7 (1) ◽

pp. 93-104 ◽

Cited By ~ 10

Author(s):

Mifodijus Sapagovas

Keyword(s):

Parabolic Equation ◽

Parabolic Equations ◽

Nonlocal Condition ◽

Nonlocal Conditions ◽

Numerical Algorithms ◽

Uniqueness Of The Solution

Numerous and different nonlocal conditions for the solvability of parabolic equations were researched in many articles and reports. The article presented analyzes such conditions imposed, and observes that the existence and uniqueness of the solution of parabolic equation is related mainly to ”smallness” of functions, involved in nonlocal conditions. As a consequence the hypothesis has been made, stating the assumptions on functions in nonlocal conditions are related to numerical algorithms of solving parabolic equations, and not to the parabolic equation itself.

Correctness conditions for high-order differential equations with unbounded coefficients

Boundary Value Problems ◽

10.1186/s13661-021-01526-5 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Kordan N. Ospanov

Keyword(s):

Differential Equation ◽

Hilbert Space ◽

Sufficient Conditions ◽

Integral Operators ◽

Order Linear Differential Equation ◽

Unbounded Coefficients ◽

Weighted Norms ◽

Linear Differential

AbstractWe give some sufficient conditions for the existence and uniqueness of the solution of a higher-order linear differential equation with unbounded coefficients in the Hilbert space. We obtain some estimates for the weighted norms of the solution and its derivatives. Using these estimates, we show the conditions for the compactness of some integral operators associated with the resolvent.

Solutions for impulsive fractional pantograph differential equation via generalized anti-periodic boundary condition

Advances in Difference Equations ◽

10.1186/s13662-020-02887-4 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Idris Ahmed ◽

Poom Kumam ◽

Jamilu Abubakar ◽

Piyachat Borisut ◽

Kanokwan Sitthithakerngkiet

Keyword(s):

Differential Equation ◽

Boundary Condition ◽

Fixed Point ◽

Fractional Differential Equation ◽

Periodic Boundary Condition ◽

Periodic Boundary ◽

Fixed Point Theorems ◽

Fractional Differential

Abstract This study investigates the solutions of an impulsive fractional differential equation incorporated with a pantograph. This work extends and improves some results of the impulsive fractional differential equation. A differential equation of an impulsive fractional pantograph with a more general anti-periodic boundary condition is proposed. By employing the well-known fixed point theorems of Banach and Krasnoselskii, the existence and uniqueness of the solution of the proposed problem are established. Furthermore, two examples are presented to support our theoretical analysis.

Lidstone–Euler Second-Type Boundary Value Problems: Theoretical and Computational Tools

Mediterranean Journal of Mathematics ◽

10.1007/s00009-021-01822-5 ◽

2021 ◽

Vol 18 (5) ◽

Author(s):

Francesco Aldo Costabile ◽

Maria Italia Gualtieri ◽

Anna Napoli

Keyword(s):

Boundary Value Problem ◽

Boundary Conditions ◽

Interpolation Problem ◽

Boundary Value ◽

Computational Tools ◽

Numerical Examples ◽

Odd Order ◽

Type Boundary

AbstractGeneral nonlinear high odd-order differential equations with Lidstone–Euler boundary conditions of second type are treated both theoretically and computationally. First, the associated interpolation problem is considered. Then, a theorem of existence and uniqueness of the solution to the Lidstone–Euler second-type boundary value problem is given. Finally, for a numerical solution, two different approaches are illustrated and some numerical examples are included to demonstrate the validity and applicability of the proposed algorithms.

Extending the Applicability of a Two-Step Chord-Type Method for Non-Differentiable Operators

Mathematics ◽

10.3390/math7090804 ◽

2019 ◽

Vol 7 (9) ◽

pp. 804

Author(s):

Ioannis K. Argyros ◽

Neha Gupta ◽

J. P. Jaiswal

Keyword(s):

Approximate Solution ◽

Convergence Analysis ◽

Banach Spaces ◽

Recurrence Relation ◽

Convergence Theorem ◽

Local Convergence ◽

Numerical Illustration ◽

Type Method ◽

Local Convergence Analysis

The semi-local convergence analysis of a well defined and efficient two-step Chord-type method in Banach spaces is presented in this study. The recurrence relation technique is used under some weak assumptions. The pertinency of the assumed method is extended for nonlinear non-differentiable operators. The convergence theorem is also established to show the existence and uniqueness of the approximate solution. A numerical illustration is quoted to certify the theoretical part which shows that earlier studies fail if the function is non-differentiable.

On Existence Theorems to Symmetric Functional Set-Valued Differential Equations

Symmetry ◽

10.3390/sym13071219 ◽

2021 ◽

Vol 13 (7) ◽

pp. 1219

Author(s):

Marek T. Malinowski

Keyword(s):

Differential Equations ◽

Existence Theorems ◽

Type Theorem ◽

Integral Representations ◽

Nonempty Compact ◽

Picard Type Theorem ◽

Convex Subsets

In this paper, we consider functional set-valued differential equations in their integral representations that possess integrals symmetrically on both sides of the equations. The solutions have values that are the nonempty compact and convex subsets. The main results contain a Peano type theorem on the existence of the solution and a Picard type theorem on the existence and uniqueness of the solution to such equations. The proofs are based on sequences of approximations that are constructed with appropriate Hukuhara differences of sets. An estimate of the magnitude of the solution’s values is provided as well. We show the closeness of the unique solutions when the equations differ slightly.

Best Proximity Point for Generalized Proximal Weak Contractions in Complete Metric Space

Journal of Applied Mathematics ◽

10.1155/2014/150941 ◽

2014 ◽

Vol 2014 ◽

pp. 1-6 ◽

Cited By ~ 4

Author(s):

Erdal Karapınar ◽

V. Pragadeeswarar ◽

M. Marudai

Keyword(s):

Approximate Solution ◽

Metric Space ◽

Metric Spaces ◽

Best Proximity Point ◽

Complete Metric Space ◽

Optimal Approximate Solution ◽

Weak Contraction ◽

Complete Metric Spaces ◽

New Class

We introduce a new class of nonself-mappings, generalized proximal weak contraction mappings, and prove the existence and uniqueness of best proximity point for such mappings in the context of complete metric spaces. Moreover, we state an algorithm to determine such an optimal approximate solution designed as a best proximity point. We establish also an example to illustrate our main results. Our result provides an extension of the related results in the literature.

NEW MODELS IN MICROPOLAR FLUID AND THEIR APPLICATION TO LUBRICATION

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s021820250500039x ◽

2005 ◽

Vol 15 (03) ◽

pp. 343-374 ◽

Cited By ~ 12

Author(s):

GUY BAYADA ◽

NADIA BENHABOUCHA ◽

MICHÈLE CHAMBAT

Keyword(s):

Boundary Condition ◽

Friction Coefficient ◽

Boundary Conditions ◽

Micropolar Fluid ◽

Reynolds Equation ◽

Slip Boundary Condition ◽

Slip Boundary ◽

New Models ◽

Uniqueness Of The Solution

A thin micropolar fluid with new boundary conditions at the fluid-solid interface, linking the velocity and the microrotation by introducing a so-called "boundary viscosity" is presented. The existence and uniqueness of the solution is proved and, by way of asymptotic analysis, a generalized micropolar Reynolds equation is derived. Numerical results show the influence of the new boundary conditions for the load and the friction coefficient. Comparisons are made with other works retaining a no slip boundary condition.

ON STOCHASTIC GENERALIZED FUNCTIONS

Infinite Dimensional Analysis Quantum Probability and Related Topics ◽

10.1142/s0219025711004407 ◽

2011 ◽

Vol 14 (02) ◽

pp. 237-260 ◽

Cited By ~ 4

Author(s):

PEDRO CATUOGNO ◽

CHRISTIAN OLIVERA

Keyword(s):

Cauchy Problem ◽

Generalized Functions ◽

Stochastic Cauchy Problem

In this work we introduce a new algebra of stochastic generalized functions. The regular Hida distributions in [Formula: see text] are embedded in this algebra via their chaos expansions. As an application, we prove the existence and uniqueness of the solution of a stochastic Cauchy problem involving singularities.