Semilinear stochastic partial differential equations: Central limit theorem and moderate deviations
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DOI: 10.1002/mma.7224
Abstract: In this paper, we establish a central limit theorem (CLT) and the moderate deviation principles (MDP) for a class of semilinear stochastic partial differential equations driven by multiplicative noise on a bounded domain. The main… read more here.
Keywords: partial differential; semilinear stochastic; central limit; stochastic partial ... See more keywords
Summability of Formal Solutions for Some Generalized Moment Partial Differential Equations
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DOI: 10.1007/s00025-020-01324-y
Abstract: The concept of moment differentiation is extended to the class of moment summable functions, giving rise to moment differential properties. The main result leans on accurate upper estimates for the integral representation of the moment… read more here.
Keywords: moment; partial differential; formal solutions; summability formal ... See more keywords
Maillet type theorem for nonlinear totally characteristic partial differential equations
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DOI: 10.1007/s00208-019-01864-x
Abstract: The paper discusses a holomorphic nonlinear singular partial differential equation $$(t \partial _t)^mu=F(t,x,\{(t \partial _t)^j \partial _x^{\alpha }u \}_{j+\alpha \le m, j read more here.
Keywords: nonlinear totally; maillet type; partial differential; totally characteristic ... See more keywords
A simple algorithm for numerical solution of nonlinear parabolic partial differential equations
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DOI: 10.1007/s00366-019-00796-z
Abstract: In this paper, numerical solution of nonlinear two-dimensional parabolic partial differential equations with initial and Dirichlet boundary conditions is considered. The time derivative is approximated using finite difference scheme whereas space derivatives are approximated using… read more here.
Keywords: partial differential; numerical solution; solution nonlinear; method ... See more keywords
Maurice Janet’s algorithms on systems of linear partial differential equations
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DOI: 10.1007/s00407-020-00255-y
Abstract: This article describes the emergence of formal methods in theory of partial differential equations (PDE) in the French school of mathematics through Janet’s work in the period 1913–1930. In his thesis and in a series… read more here.
Keywords: partial differential; algorithms systems; janet algorithms; differential equations ... See more keywords
Gaussian process for estimating parameters of partial differential equations and its application to the Richards equation
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DOI: 10.1007/s00477-019-01709-8
Abstract: This paper proposes a new collocation method for estimating parameters of a partial differential equation (PDE), which uses Gaussian process (GP) as a basis function and is termed as Gaussian process for partial differential equation… read more here.
Keywords: partial differential; estimating parameters; method; equation ... See more keywords
Neural networks catching up with finite differences in solving partial differential equations in higher dimensions
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DOI: 10.1007/s00521-020-04743-8
Abstract: Solving partial differential equations using neural networks is mostly a proof of concept approach. In the case of direct function approximation, a single neural network is constructed to be the solution of a particular boundary… read more here.
Keywords: partial differential; neural networks; finite differences; solution ... See more keywords
Ambient residual penalty approximation of partial differential equations on embedded submanifolds
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DOI: 10.1007/s10444-020-09802-1
Abstract: In this paper, we present a novel approach to the approximate solution of elliptic partial differential equations on compact submanifolds of ℝ d $\mathbb {R}^{d}$ , particularly compact surfaces and the surface equation Δ M… read more here.
Keywords: partial differential; penalty approximation; penalty; residual penalty ... See more keywords
Dichotomy of Linear Partial Differential Equations of Neutral Type in Banach Spaces
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DOI: 10.1007/s10884-020-09864-1
Abstract: This present paper is mainly devoted to investigate the property of spectral decomposition of neutral differential equations in infinite dimensional setting, that is the exponential dichotomy. In fact, we prove that the exponential dichotomy of… read more here.
Keywords: partial differential; dichotomy linear; neutral type; equations neutral ... See more keywords
A Projection Method for the Conservative Discretizations of Parabolic Partial Differential Equations
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DOI: 10.1007/s10915-017-0536-2
Abstract: We present a projection method for the conservative discretizations of parabolic partial differential equations. When we solve a system of discrete equations arising from the finite difference discretization of the PDE, we can use iterative… read more here.
Keywords: partial differential; method conservative; discretizations parabolic; parabolic partial ... See more keywords
Adaptive Concepts for Stochastic Partial Differential Equations
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DOI: 10.1007/s10915-019-00944-z
Abstract: An adaptive time stepping method to numerically provide approximate weak approximations of solutions of general SPDEs is proposed, where local step sizes are chosen in regard of the distance between empirical laws of subsequent time… read more here.
Keywords: concepts stochastic; stochastic partial; time; partial differential ... See more keywords