In this study, Reduced Differential Transform Method (RDTM) is applied to some systems of nonlinear PDEs. The concept of RDTM is introduced birefly and RDTM is examined for system of nonlinear PDEs. The main advantage of the RDTM is the fact that it provides to its user an analytical approximation, in many cases an exact solution, in a rapidly convergent sequence with elegantly computed terms. ...

reduced differental transform method (rdtm), which isone of the useful and effective numerical method, is applied to solve nonlinear time-dependent foam drainage equation (fde) with different initial conditions. we compare our method with the famous adomian decomposition and laplace decomposition methods. the obtained resultsdemonstrated that rdtm is a powerful tool for solving nonlinear par...

The classical Feynman-Kac formula states the connection between linear parabolic partial differential equations (PDEs), like the heat equation, and expectation of stochastic processes driven by Brownian motion. It gives then a method for solving linear PDEs by Monte Carlo simulations of random processes. The extension to (fully)nonlinear PDEs led in the recent years to important developments in...

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...

Ear modeling can significantly improve sound signal processing and the design of hearing devices. Ear models based on mechanics and neural phenomenology of the inner ear (cochlea) form a class of nonlinear nonlocal dispersive partial differential equations (PDEs). These PDEs capture the essential nonlinear phenomena in hearing, such as combination frequency generation, compression, and suppress...

A class of solvable (systems of) nonlinear evolution PDEs in multidimensional space is discussed. We focus on a rotation-invariant system of PDEs of Schrödinger type and on a relativistically-invariant system of PDEs of Klein–Gordon type. Isochronous variants of these evolution PDEs are also considered.

Multiscale signal analysis has been used since the early 1990s as a powerful tool for image processing. Nonlinear PDEs and multiscale morphological filters can be used to create nonlinear operators that have advantages over linear operators, notably preserving important features such as edges in images. In this report, we present the nonlinear Hamilton-Jacobi PDEs commonly used as filters for i...