相关论文: A Non-Iterative Transformation Method for an Exten…
In this paper, we introduce a novel semi-analytical method for solving a broad class of initial value problems involving differential, integro-differential, and delay equations, including those with fractional and variable-order…
A three-point iterative method for solving scalar non-linear equations was selected and then adapted to solve systems of non-linear equations. Subsequently, by applying Taylor's theorem to functions of $\R^{n}$ in $\R^{n}$, it is shown that…
In this work, we propose a non-iterative Gaussian transformation strategy based on copula function, which doesn't require some commonly seen restrictive assumptions in the previous studies such as the elliptically symmetric distribution…
We present an extension of two policy-iteration based algorithms on weighted graphs (viz., Markov Decision Problems and Max-Plus Algebras). This extension allows us to solve the following inverse problem: considering the weights of the…
Scalar extrapolation and convergence acceleration methods are central tools in numerical analysis for improving the efficiency of iterative algorithms and the summation of slowly convergent series. These methods construct transformed…
In this paper we propose an extension of the iteratively regularized Gauss--Newton method to the Banach space setting by defining the iterates via convex optimization problems. We consider some a posteriori stopping rules to terminate the…
The aim of this paper is to introduce a new Newton-type iterative method and then to show that this process converges to the unique solution of the scalar nonlinear equation f(x)=0 under weaker conditions involving only f and f' by fixed…
Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems for partial differential equations. When considering non-stationary problems,…
In this paper, we study a fast approximate inference method based on expectation propagation for exploring the posterior probability distribution arising from the Bayesian formulation of nonlinear inverse problems. It is capable of…
The variational approach to fracture is effective for simulating the nucleation and propagation of complex crack patterns, but is computationally demanding. The model is a strongly nonlinear non-convex variational inequality that demands…
Aim of this paper is the qualitative analysis of the solution of a boundary value problem for a third-order non linear parabolic equation which describes several dissipative models. When the source term is linear, the problem is explictly…
In this work, we consider a boundary value problem for nonlinear triharmonic equation. Due to the reduction of nonlinear boundary value problems to operator equation for nonlinear terms we establish the existence, uniqueness and positivity…
Variable-exponent fractional models attract increasing attentions in various applications, while the rigorous analysis is far from well developed. This work provides general tools to address these models. Specifically, we first develop a…
In this paper we show existence of solutions for some elliptic problems with nonlocal diffusion by means of nonvariational tools. Our proof is based on the use of topological degree, which requires a priori bounds for the solutions. We…
An initial-boundary value problem for a time-fractional subdiffusion equation with an arbitrary order elliptic differential operator is considered. Uniqueness and existence of the classical solution of the posed problem are proved by the…
This paper systematically explains how to apply the invariant subspace method using variable transformation for finding the exact solutions of the (k+1)-dimensional nonlinear time-fractional PDEs in detail. More precisely, we have shown how…
A new method for solving stiff boundary value problems is described and compared to other known approaches using the Troesch's problem as a test example. The method is based on the general idea of alternate approximation of either the…
This work applies modern AI tools (transformers) to solving one of the oldest statistical problems: Poisson means under empirical Bayes (Poisson-EB) setting. In Poisson-EB a high-dimensional mean vector $\theta$ (with iid coordinates…
Solving complex optimization problems in engineering and the physical sciences requires repetitive computation of multi-dimensional function derivatives. Commonly, this requires computationally-demanding numerical differentiation such as…
The paper deals with a boundary value problem for the nonlinear integro-differential equation $u^{\prime\prime\prime\prime}-m\left(\int_0^l {u^\prime}^2dx\right)u^{\prime\prime}=f(x,u,u^\prime), \; m(z)\geq \alpha>0, \; 0\leq z <\infty$,…