A solution method for autonomous first-order algebraic partial differential equations in several variables

نویسندگان

  • Georg Grasegger
  • Franz Winkler
  • Alberto Lastra
  • J. Rafael Sendra
چکیده

In this paper we present a procedure for solving first-order autonomous algebraic partial differential equations in an arbitrary number of variables. The method uses rational parametrizations of algebraic (hyper)surfaces and generalizes a similar procedure for first-order autonomous ordinary differential equations. In particular we are interested in rational solutions and present certain classes of equations having rational solutions. However, the method can also be used for finding non-rational solutions.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A solution method for autonomous first-order algebraic partial differential equations

In this paper we present a procedure for solving first-order autonomous algebraic partial differential equations. The method uses rational parametrizations of algebraic surfaces and generalizes a similar procedure for first-order autonomous ordinary differential equations. In particular we are interested in rational solutions and present certain classes in which such solutions exist. However, t...

متن کامل

Solving high-order partial differential equations in unbounded domains by means of double exponential second kind Chebyshev approximation

In this paper, a collocation method for solving high-order linear partial differential equations (PDEs) with variable coefficients under more general form of conditions is presented. This method is based on the approximation of the truncated double exponential second kind Chebyshev (ESC) series. The definition of the partial derivative is presented and derived as new operational matrices of der...

متن کامل

On Symbolic Solutions of Algebraic Partial Differential Equations

In this paper we present a general procedure for solving first-order autonomous algebraic partial differential equations in two independent variables. The method uses proper rational parametrizations of algebraic surfaces and generalizes a similar procedure for first-order autonomous ordinary differential equations. We will demonstrate in examples that, depending on certain steps in the procedu...

متن کامل

Simulation of Singular Fourth- Order Partial Differential Equations Using the Fourier Transform Combined With Variational Iteration Method

In this paper, we present a comparative study between the modified variational iteration method (MVIM) and a hybrid of Fourier transform and variational iteration method (FTVIM). The study outlines the efficiencyand convergence of the two methods. The analysis is illustrated by investigating four singular partial differential equations with variable coefficients. The solution of singular partia...

متن کامل

An algebraic calculation method for describing time-dependent processes in electrochemistry – Expansion of existing procedures

In this paper an alternative model allowing the extension of the Debye-Hückel Theory (DHT) considering time dependence explicitly is presented. From the Electro-Quasistatic approach (EQS) introduced in earlier studies time dependent potentials are suitable to describe several phenomena especially conducting media as well as the behaviour of charged particles (ions) in electrolytes. This leads t...

متن کامل

ذخیره در منابع من

ذخیره در منابع من قبلا به منابع من ذحیره شده

{@ msg_add @}


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2015