Related papers: A multiple exp-function method for nonlinear diffe…
We use trivariate spline functions for the numerical solution of the Dirichlet problem of the 3D elliptic Monge-Amp\'ere equation. Mainly we use the spline collocation method introduced in [SIAM J. Numerical Analysis, 2405-2434,2022] to…
One of old methods for finding exact solutions of nonlinear differential equations is considered. Modifications of the method are discussed. Application of the method is illustrated for finding exact solutions of the Fisher equation and…
In this paper numerical methods for solving stochastic differential equations with Markovian switching (SDEwMSs) are developed by pathwise approximation. The proposed family of strong predictor-corrector Euler-Maruyama methods is designed…
We present an extension of the Piecewise Parabolic Method to special relativistic fluid dynamics in multidimensions. The scheme is conservative, dimensionally unsplit, and suitable for a general equation of state. Temporal evolution is…
In this article we present first an algorithm for calculating the determining equations associated with so-called ``nonclassical method'' of symmetry reductions (a la Bluman and Cole) for systems of partial differentail equations. This…
This note shows that in looking for exact solutions to nonlinear PDEs, the direct method of functional separation of variables can, in certain cases, be more effective than the method of differential constraints based on the compatibility…
We consider the initial/boundary value problem for the fractional diffusion and diffusion-wave equations involving a Caputo fractional derivative in time. We develop two "simple" fully discrete schemes based on the Galerkin finite element…
This paper is an attempt to solve an important class of hypersingular integral equations of the second kind. To this end, we apply a new weighted and modified perturbation method which includes some special cases of the Adomian…
We apply pseudo-spectral methods to integrate functional flow equations with high accuracy, extending earlier work on functional fixed point equations \cite{Borchardt:2015rxa}. The advantages of our method are illustrated with the help of…
This survey provides an overview of state-of-the art multirate schemes, which exploit the different time scales in the dynamics of a differential equation model by adapting the computational costs to different activity levels of the system.…
We present the algorithms for three popular methods: F-expansion, modified F-expansion, and first integral methods to automatically get closed-form traveling-wave solutions of nonlinear partial differential equations (NLPDEs). We generalize…
High frequency integral equation methodologies display the capability of reproducing single-scattering returns in frequency-independent computational times and employ a Neumann series formulation to handle multiple-scattering effects. This…
We apply the method of simplest equation for obtaining exact solitary traveling-wave solutions of nonlinear partial differential equations that contain monomials of odd and even grade with respect to participating derivatives. We consider…
The basic ideas of a homotopy-based multiple-variable method is proposed and applied to investigate the nonlinear interactions of periodic traveling waves. Mathematically, this method does not depend upon any small physical parameters at…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
This contribution investigates the connection between isogeometric analysis and integral equation methods for full-wave electromagnetic problems up to the low-frequency limit. The proposed spline-based integral equation method allows for an…
In this paper invariant subspace method has been employed for solving linear and non-linear fractional partial differential equations involving Caputo derivative. A variety of illustrative examples are solved to demonstrate the…
In the present paper invariant subspace method has been extended for solving systems of multi-term fractional partial differential equations (FPDEs) involving both time and space fractional derivatives. Further the method has also been…
An explicit multistep scheme is proposed for solving the initial-value Wigner problem. In this scheme, the integrated form of the Wigner equation is approximated by extrapolation or interpolation polynomials on backwards characteristics,…
This paper is concerned with the periodic (in time) solutions to an one-dimensional semilinear wave equation with $x$-dependent coefficient. Such a model arises from the forced vibrations of a nonhomogeneous string and propagation of…