Displaying similar documents to “A finite difference method for quasi-linear and nonlinear differential functional parabolic equations with Dirichlet's condition”

Difference methods for parabolic functional differential problems of the Neumann type

K. Kropielnicka (2007)

Annales Polonici Mathematici

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Nonlinear parabolic functional differential equations with initial boundary conditions of the Neumann type are considered. A general class of difference methods for the problem is constructed. Theorems on the convergence of difference schemes and error estimates of approximate solutions are presented. The proof of the stability of the difference functional problem is based on a comparison technique. Nonlinear estimates of the Perron type with respect to the functional variable for given...

Implicit difference methods for nonlinear first order partial functional differential systems

Elżbieta Puźniakowska-Gałuch (2010)

Applicationes Mathematicae

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Initial problems for nonlinear hyperbolic functional differential systems are considered. Classical solutions are approximated by solutions of suitable quasilinear systems of difference functional equations. The numerical methods used are difference schemes which are implicit with respect to the time variable. Theorems on convergence of difference schemes and error estimates of approximate solutions are presented. The proof of the stability is based on a comparison technique with nonlinear...

Implicit difference methods for quasilinear parabolic functional differential problems of the Dirichlet type

K. Kropielnicka (2008)

Applicationes Mathematicae

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Classical solutions of quasilinear functional differential equations are approximated with solutions of implicit difference schemes. Proofs of convergence of the difference methods are based on a comparison technique. Nonlinear estimates of the Perron type with respect to the functional variable for given functions are used. Numerical examples are given.

Comparison of explicit and implicit difference methods for quasilinear functional differential equations

W. Czernous, Z. Kamont (2011)

Applicationes Mathematicae

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We give a theorem on error estimates of approximate solutions for explicit and implicit difference functional equations with unknown functions of several variables. We apply this general result to investigate the stability of difference methods for quasilinear functional differential equations with initial boundary condition of Dirichlet type. We consider first order partial functional differential equations and parabolic functional differential problems. We compare the properties...

Symmetric interior penalty discontinuous Galerkin method for nonlinear fully coupled quasi-static thermo-poroelasticity problems

Fan Chen, Ming Cui, Chenguang Zhou (2025)

Applications of Mathematics

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We propose a symmetric interior penalty discontinuous Galerkin (DG) method for nonlinear fully coupled quasi-static thermo-poroelasticity problems. Firstly, a fully implicit nonlinear discrete scheme is constructed by adopting the DG method for the spatial approximation and the backward Euler method for the temporal discretization. Subsequently, the existence and uniqueness of the solution of the numerical scheme is proved, and then we derive the a priori error estimate for the three...

Semi-analytical approach to initial problems for systems of nonlinear partial differential equations with constant delay

Šamajová, Helena

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This paper deals with the differential transform method for solving of an initial value problem for a system of two nonlinear functional partial differential equations of parabolic type. We consider non-delayed as well as delayed types of coupling and the different variety of initial functions are thought over. The convergence of solutions and the error estimation to the presented procedure is studied. Two numerical examples for non-delayed and delayed systems are included.

Implicit difference schemes for mixed problems related to parabolic functional differential equations

Milena Netka (2011)

Annales Polonici Mathematici

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Solutions of initial boundary value problems for parabolic functional differential equations are approximated by solutions of implicit difference schemes. The existence and uniqueness of approximate solutions is proved. The proof of the stability is based on a comparison technique with nonlinear estimates of the Perron type for given operators. It is shown that the new methods are considerably better than the explicit difference schemes. Numerical examples are presented.

The quasilinear parabolic kirchhoff equation

Łukasz Dawidowski (2017)

Open Mathematics

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In this paper the existence of solution of a quasilinear generalized Kirchhoff equation with initial – boundary conditions of Dirichlet type will be studied using the Leray – Schauder principle.

Existence of explosive solutions to some nonlinear parabolic Itô equations

Pao-Liu Chow (2015)

Banach Center Publications

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The paper is concerned with the problem of existence of explosive solutions for a class of nonlinear parabolic Itô equations. Under some sufficient conditions on the initial state and the coefficients, it is proven by the method of auxiliary functionals that there exist explosive solutions with positive probability. The main results are presented in Theorems 3.1 and 3.2 under different sets of conditions. An example is given to illustrate some application of the second theorem. ...

Integro-differential systems with variable exponents of nonlinearity

Oleh Buhrii, Nataliya Buhrii (2017)

Open Mathematics

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Some nonlinear integro-differential equations of fourth order with variable exponents of the nonlinearity are considered. The initial-boundary value problem for these equations is investigated and the existence theorem for the problem is proved.