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We present a new procedural incompressible velocity field authoring tool, which lets users design a volumetric flow by directly specifying velocity along control curves. Our method combines the Method of Regularized Stokeslets with Galerkin ...

In this article, we discuss the convergence analysis of the classical first-order and fractional-order Volterra integro-differential equations of the second kind with a smooth kernel by reducing them into a system of fractional Fredholm integro-...

• Projection methods proposed for fractional Volterra integro-differential equation.
• Superconvergent results obtained for all β ∈ (0, 1] without any limiting condition.
• The convergence rates increase with the increasing order of ...

The main crux of this manuscript is to study the existence of weak solutions for the following fractional double phase elliptic problem with Dirichlet boundary conditions $$\begin{array}{c}\hfill \left\{\begin{array}{cc}{(-\mathrm{\Delta })}_p^{\sigma }w+{(-\mathrm{\Delta })}_q^{\sigma }w=\psi (z)+g(z,w)\hfill & \text{in}\mathrm{\Theta },\hfill \\ w=0,\hfill & \text{on}{\mathbb{R}}^N\backslash \mathrm{\Theta },\hfill \end{array}\right)\end{array}$$where $1<p<q<\frac{N}{\sigma }$, $\sigma \in (0,1)$ and ${(-\mathrm{\Delta })}_p^{\sigma },...{\mathrm{}}_{}^{}$$\mathit{}$

This study investigates a system of second-kind nonlinear Fredholm integral equations (SSNFIEs) featuring a Green's type kernel function. To solve this integral equations (IEs), we introduce Galerkin and iterated Galerkin (IG) methods based on ...

• A system of second-kind coupled nonlinear Fredholm integral equations with Green's type kernel functions are solved.
• Effective Galerkin methods and iterated Galerkin method are proposed for SSNFIE with Green's type kernel function.

A theoretical and computational finite element study of a thermal non-equilibrium model governed by modified Navier-Stokes equations coupled with energy conservation governing the flow and heat transfer in a complex hybrid nanofluid saturated ...

We couple the L1 discretization of the Caputo fractional derivative in time with the Galerkin scheme to devise a linear numerical method for the semilinear subdiffusion equation. Two important points that we make are nonsmooth initial data and ...

In this paper, we propose and analyse a numerical method to solve 2D Dirichlet time-harmonic elastic wave equations. The procedure is based on the decoupling of the elastic vector field into scalar Pressure (P-) and Shear (S-) waves via a ...

The paper addresses a computational method to simulate more accurate models for population growth with immigration, focusing on integral equations (IEs) featuring a delay parameter in the time variable. The proposed method utilizes Legendre ...

A convection–diffusion problem with a large shift in space is considered. Numerical analysis of high order finite element methods on layer-adapted Durán type meshes, as well as on coarser Durán type meshes in places where weak layers appear, is ...

For finite-strain problems of quasi-incompressible materials, with hyperelastic and hyperelasto-plastic behavior, we develop a mixed polynomial-enriched radial-basis function (RBF) interpolation. It is characterized by decoupling quadrature and ...

• Selective quadrature/interpolation finite-strain formulation based on enriched RBF with hyperelasticity/plasticity.
• Compact-support RBFs enriched with a polynomial basis.
• Outstanding results for quasi-incompressible problems with ...

Finite element analysis of combined mass, momentum, and energy conservation of hybrid nanofluid is of great industrial value. This work provides a theoretical and computational finite element study of modified Navier-Stokes Equations coupled with ...

In this paper, we develop a fully discrete fast multiscale Galerkin method for solving the boundary integral equation derived from the interior Dirichlet problem in a domain with corners. The integral operator in the equation can be split into two ...$\mathcal{}{\mathrm{}}^{}$${\mathrm{}}^{}$

We study a mathematical model of a viscous compressible fluid obeying the slip boundary condition of friction type. We present a notion of weak solutions to this model, in which the momentum equation and the associated energy inequality are ...

In this paper, we employ Tikhonov regularization method with the projection methods using Jacobi polynomial bases to the first kind of Fredholm integral equations to find the approximate solution. We discuss the convergence analysis and obtain the ...${\mathit{}}_{{\mathit{}}^{\mathit{}\mathbf{}\mathit{}}}^{\mathbf{}}$

This paper focuses on the computational study of seventh-order KdV equations via the quintic B-spline (QBS) finite element method (FEM). The KdV equations contain higher-order derivative terms. We transform the higher order into lower ...

In this article, we apply Jacobi spectral Galerkin, multi-Galerkin methods and their iterated versions to approximate the system of Volterra integral equations for smooth as well as weakly singular kernels and obtain the ...

We consider a swelling porous elastic system with a single nonlinear variable exponent damping. We establish the existence result using the Faedo–Galerkin approximations method, and then, we prove that the system is stable under a natural ...

In the present research, the two-dimensional Volterra–Fredholm integro-differential (2D-VFID) equations of fractional order are studied through utilizing a new scheme based on the two-dimensional normalized Müntz–Legendre​ polynomials (...

In advanced process, electromagnetic coupling among interconnect wires plays an increasingly important role in signoff analysis. For VLSI chip design, the requirement of fast and accurate capacitance extraction is becoming more and more urgent. And the ...

Adaptive Galerkin numerical schemes integrate time-dependent partial differential equations with a finite number of basis functions, and a subset of them is selected at each time step. This subset changes over time discontinuously according to the ...