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This paper introduced a way of fractal to solve the problem of taking count of the integer partitions, furthermore, using the method in this paper some recurrence equations concerning the integer partitions can be deduced, including the…
In this work, we present an algorithm for the diagonalization of the Integration-by-Parts (IBP) equations. Diagonalized IBP equations are indispensable for reducing loop integrals with high numerator powers to master integrals and for…
The purpose of this paper is to propose a semi-analytical technique convenient for numerical approximation of solutions of the initial value problem for $p$-dimensional delayed and neutral differential systems with constant, proportional…
For the quadratic Lagrange interpolation function, an algorithm is proposed to provide explicit and verified bound for the interpolation error constant that appears in the interpolation error estimation. The upper bound for the…
The article is devoted to the integration order replacement technique for iterated Ito stochastic integrals and iterated stochastic integrals with respect to martingales. We consider the class of iterated Ito stochastic integrals, for which…
This paper presents a universal numerical scheme tailored for tackling linear integral, integro-differential, and both initial and boundary value problems of ordinary differential equations. The numerical scheme is readily adapted for…
For solving linear ill-posed problems regularization methods are required when the right hand side is with some noise. In the present paper regularized solutions are obtained by implicit iteration methods in Hilbert scales. % By exploiting…
This paper considers the extension of classical Lagrange interpolation in one real or complex variable to "polynomials of one quaternionic variable". To do this we develop some aspects of the theory of such polynomials. We then give a…
A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…
Interpolation theory for complex polynomials is well understood. In the non-commutative quaternionic setting, the polynomials can be evaluated "on the left" and "on the right". If the interpolation problem involves interpolation conditions…
We show that integro-differential generalized Langevin and non-Markovian master equations can be transformed into larger sets of ordinary differential equations. .On the basis of this transformation we develop a numerical method for solving…
In this paper we consider a fully third order nonlinear boundary value problem which is of great interest of many researchers. First we establish the existence, uniqueness of solution. Next, we propose simple iterative methods on both…
This article is the third and last of a series presenting an alternative method to compute the one-loop scalar integrals. It extends the results of first two articles to the infrared divergent case. This novel method enjoys a couple of…
An important problem that arises in many engineering applications is the boundary value problem for ordinary differential equations. There have been many computational methods proposed for dealing with this problem. The convergence of the…
This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…
We are concerned with the numerical resolution of backward stochastic differential equations. We propose a new numerical scheme based on iterative regressions on function bases, which coefficients are evaluated using Monte Carlo…
We propose a characterization of a $p$-Laplace higher eigenvalue based on the inverse iteration method with balancing the Rayleigh quotients of the positive and negative parts of solutions to consecutive $p$-Poisson equations. The approach…
In some fields such as Mathematics Mechanization, automated reasoning and Trustworthy Computing etc., exact results are needed. Symbolic computations are used to obtain the exact results. Symbolic computations are of high complexity. In…
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,…
Traditional numerical techniques for solving time-dependent partial-differential-equation (PDE) initial-value problems (IVPs) store a truncated representation of the function values and some number of their time derivatives at each time…