A New Numerical Approach for the Solutions of Partial Differential Equations in Three-Dimensional Space

2016 ◽  
Vol 10 (5) ◽  
pp. 1663-1672 ◽  
Author(s):  
Brajesh Kumar Singh ◽  
Carlo Bianca
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Numerical Approach ◽  
Partial Differential ◽  
Three Dimensional Space

scholarly journals New Approach for Solving Three Dimensional Space Partial Differential Equation

2019 ◽  
Vol 16 (3(Suppl.)) ◽  
pp. 0786 ◽  
Author(s):  
Enadi Et al.
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Partial Differential ◽  
Transform Method ◽  
New Approach ◽  
Practical Implications ◽  
Three Dimensional Space

This paper presents a new transform method to solve partial differential equations, for finding suitable accurate solutions in a wider domain. It can be used to solve the problems without resorting to the frequency domain. The new transform is combined with the homotopy perturbation method in order to solve three dimensional second order partial differential equations with initial condition, and the convergence of the solution to the exact form is proved. The implementation of the suggested method demonstrates the usefulness in finding exact solutions. The practical implications show the effectiveness of approach and it is easily implemented in finding exact solutions.        Finally, all algorithms in this paper are implemented in MATLAB version 7.12.

scholarly journals GROUP PROPERTIES OF A ONE-DIMENSIONAL NONLINEAR POROELASTICITY EQUATION

2019 ◽  
Vol 4 (1) ◽  
pp. 149-155
Author(s):  
Kholmatzhon Imomnazarov ◽  
Ravshanbek Yusupov ◽  
Ilham Iskandarov
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Lie Algebra ◽  
Three Dimensional ◽  
Group Classification ◽  
Second Order ◽  
Partial Differential ◽  
One Dimensional ◽  
Preliminary Group

This paper studies a class of partial differential equations of second order , with arbitrary functions and , with the help of the group classification. The main Lie algebra of infinitely infinitesimal symmetries is three-dimensional. We use the method of preliminary group classification for obtaining the classifications of these equations for a one-dimensional extension of the main Lie algebra.

The Invariant Subspace Method for Solving Fractional Partial Differential Equations

2020 ◽  
pp. 267-282
Author(s):  
Mohamed Soror Abdel Latif ◽  
Abass Hassan Abdel Kader
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Invariant Subspace ◽  
Three Dimensional ◽  
Variable Coefficients ◽  
Subspace Method ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Balance Principle ◽  
New Exact Solutions

In this chapter, the authors discuss the effectiveness of the invariant subspace method (ISM) for solving fractional partial differential equations. For this purpose, they have chosen a nonlinear time fractional partial differential equation (PDE) with variable coefficients to be investigated through this method. One-, two-, and three-dimensional invariant subspace classifications have been performed for this equation. Some new exact solutions have been obtained using the ISM. Also, the authors give a comparison between this method and the homogeneous balance principle (HBP).

scholarly journals An efficient numerical approach for space fractional partial differential equations

2020 ◽  
Vol 59 (5) ◽  
pp. 2911-2919
Author(s):  
Rabia Shikrani ◽  
M.S. Hashmi ◽  
Nargis Khan ◽  
Abdul Ghaffar ◽  
Kottakkaran Sooppy Nisar ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Approach ◽  
Fractional Partial Differential Equations ◽  
Partial Differential

A Mixed Method in Elasticity

1977 ◽  
Vol 44 (1) ◽  
pp. 51-56 ◽  
Author(s):  
N. S. V. Kameswara Rao ◽  
Y. C. Das
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Elastic Body ◽  
Mixed Method ◽  
Forced Vibration ◽  
Three Dimensional ◽  
Dynamic Problems ◽  
Partial Differential ◽  
Theory Of Plates

A mixed method for three-dimensional elasto-dynamic problems has been formulated which gives a complete choice in prescribing the boundary conditions in terms of either stresses, or displacements, or partly stresses and partly displacements. The general expressions for the responses of the elastic body have been derived in the form of transcendental partial differential equations of a set of initial functions, which can be evaluated in terms of the prescribed boundary conditions. The method so-formulated has been illustrated by applying it to the theory of plates. Only plates subjected to antisymmetric loads have been considered for illustration. Some examples of free and forced vibration of plates have been presented. Results are compared with solutions from existing theories.

STEADY FLOW OF FLUIDS WITH SHEAR-DEPENDENT VISCOSITY UNDER MIXED BOUNDARY VALUE CONDITIONS IN POLYHEDRAL DOMAINS

2000 ◽  
Vol 10 (05) ◽  
pp. 629-650 ◽  
Author(s):  
C. EBMEYER
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Steady Flow ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Three Dimensional ◽  
Partial Differential ◽  
Shear Dependent Viscosity ◽  
Polyhedral Domain ◽  
Dependent Viscosity

In this paper the system of partial differential equations [Formula: see text] is studied, where e is the symmetrized gradient of u, and T has p-structure for some p<2 (e.g. div T is the p-Laplacian and p<2). Mixed boundary value conditions on a three-dimensional polyhedral domain are considered. Ws,p-regularity (s=3/2-ε) of the velocity u and Wr,p′-regularity of the pressure π are proven.

scholarly journals Compressible, Turbulent, Viscous Flow Computations for Blade Aerodynamic and Heat Transfer

1996 ◽  
Author(s):  
A. A. Boretti
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Reynolds Number ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Viscous Flow ◽  
Three Dimensional ◽  
Time Dependent ◽  
Navier Stokes ◽  
Partial Differential

The paper presents a computer code for steady and unsteady, three-dimensional, compressible, turbulent, viscous flow simulations. The mathematical model is based on the Favre-averaged Navier-Stokes conservation equations, closed by a statistical model of turbulence. Turbulence effects are represented by using a low Reynolds number K-ω model. The numerical model makes use of a finite difference approximation in generalized coordinates for space discretization. The solution of time-dependent, three-dimensional, non-homogeneous, partial differential equations is obtained by solving, in a prescribed, symmetric pattern, three time-dependent, one-dimensional, homogeneous partial differential equations, representing convection and diffusion along each generalized coordinate direction, and one ordinary differential equation, representing generation and destruction. An explicit, multi-step, dissipative, Runge-Kutta scheme is finally adopted for time discretization. The code is applied to simulate the flow through a linear cascade of turbine rotor blades, where detailed experimental data are available. Blade aerodynamic and heat transfer are computed, at variable Reynolds and Mach numbers and turbulence levels, and compared with experimental data. While the aerodynamic prediction is relatively unaffected by the properties of both mathematical and numerical models, the heat transfer prediction proves to be extremely sensitive to models details. Low Reynolds number K-ω turbulence models theoretically reproduce laminar, turbulent and transitional boundary layers. However, their practical use in a Navier-Stokes code does not allow to entirely capture the effects of turbulence intensity and Mach and Reynolds numbers on blade heat transfer.

scholarly journals On conditions of solvability of three-dimensional integralsystem in quadratures

2017 ◽  
Vol 21 (10) ◽  
pp. 40-46
Author(s):  
E.A. Sozontova
Keyword(s):  
Differential Equations ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Original System ◽  
Goursat Problem ◽  
System Of Differential Equations ◽  
Third Order ◽  
First Order ◽  
Three Dimensional Space

In this paper we consider the system of equations with partial integrals in three-dimensional space. The purpose is to find sufficient conditions of solvability of this system in quadratures. The proposed method is based on the reduction of the original system, first, to the Goursat problem for a system of differential equations of the first order, and after that to the three Goursat problems for differential equations of the third order. As a result, the sufficient conditions of solvability of the considering system in explicit form were obtained. The total number of cases discussing solvability is 16.

scholarly journals Variational symmetries and pluri-Lagrangian structures for integrable hierarchies of PDEs

2020 ◽  
Author(s):  
Matteo Petrera ◽  
Mats Vermeeren
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Integrable Hierarchies ◽  
Dimensional Space ◽  
Original System ◽  
Lagrange Equations ◽  
Partial Differential ◽  
Dimensional Space Time ◽  
Variational Symmetries ◽  
Nonlinear Math

Abstract We investigate the relation between pluri-Lagrangian hierarchies of 2-dimensional partial differential equations and their variational symmetries. The aim is to generalize to the case of partial differential equations the recent findings in Petrera and Suris (Nonlinear Math. Phys. 24(suppl. 1):121–145, 2017) for ordinary differential equations. We consider hierarchies of 2-dimensional Lagrangian PDEs (many of which have a natural $$(1\,{+}\,1)$$ ( 1 + 1 ) -dimensional space-time interpretation) and show that if the flow of each PDE is a variational symmetry of all others, then there exists a pluri-Lagrangian 2-form for the hierarchy. The corresponding multi-time Euler–Lagrange equations coincide with the original system supplied with commuting evolutionary flows induced by the variational symmetries.

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