Mathematical models containing partial differential equations (PDEs) occur in many engineering applications. Modelica is a general, high-level language for object-oriented modeling with differential-algebraic equations (DAEs). There is a need for extending Modelica to also support modeling with PDEs. This paper presents some ideas on such extensions to the Modelica language, that would allow fo...

in this paper, first the properties of one and two-dimensional differential transforms are presented.next, by using the idea of differential transform, we will present a method to find an approximate solution fora volterra integro-partial differential equations. this method can be easily applied to many linear andnonlinear problems and is capable of reducing computational works. in some particu...

Proper orthogonal decomposition is a popular approach for determining the principal spatial structures from the measured data. Generally, model reduction using empirical eigenfunctions (EEFs) can generate a relatively low-dimensional model among all linear expansions. However, the neglectful modes representing only a tiny amount of energy will be crucial in the modeling for certain type of nonl...

The Mathematica implementation of the tanh and sech-methods for computing exact travelling wave solutions of nonlinear partial differential equations (PDEs) is presented. These methods also apply to ordinary differential equations (ODEs). New algorithms are given to compute polynomial solutions of ODEs and PDEs in terms of the Jacobi elliptic functions. An adaptation of the tanh-method to nonli...

Differential constraints are used as a means of developing a systematic method for finding exact solutions to quasilinear nonautonomous hyperbolic systems of first-order partial differential equations (PDEs) involving two independent variables. The leading assumption of the hyperbolicity of the basic system together with a strict compatibility argument permits characterization of the most gener...

In this paper, a general framework for surface modeling using geometric partial differential equations (PDEs) is presented. Starting with a general integral functional, we derive an Euler–Lagrange equation and then a geometric evolution equation (also known as geometric flow). This evolution equation is universal, containing several well-known geometric partial differential equations as its spe...

This paper presents an approach to modelling distributed systems described by Partial Differential Equations(PDEs) in SystemC-A. Such modeling approach is quite important because of the modeling difficulties for the mixedphysical domain systems where complex digital and analogue electronics interfaces with vital distributed physical effects. As current SystemC-A does not support PDEs modeling, ...

a simple new closed form of the green function for axisymmetric magnetostatic problemsis found analytically in cylindrical coordinates. the result is verified by applying several examples.

in this paper, a high-order and conditionally stable stochastic difference scheme is proposed for the numerical solution of $rm ithat{o}$ stochastic advection diffusion equation with one dimensional white noise process. we applied a finite difference approximation of fourth-order for discretizing space spatial derivative of this equation. the main properties of deterministic difference schemes,...

We show that matrix Q × Q Self-dual type S-integrable Partial Differential Equations (PDEs) possess a family of lower-dimensional reductions represented by the matrix Q × n 0 Q quasilinear first order PDEs solved in [29] by the method of characteristics. In turn, these PDEs admit two types of available particular solutions: (a) explicit solutions and (b) solutions described implicitly by a syst...