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Mitigating the impact of waves leaving a numerical domain has been a persistent challenge in numerical modeling. Reducing wave reflection at the domain boundary is crucial for accurate simulations. Absorbing layers, while common, often…
In this paper, we solve Laplace equation analytically by using differential transform method. For this purpose, we consider four models with two Dirichlet and two Neumann boundary conditions and obtain the corresponding exact solutions. The…
We present a new method for the numerical solution of singular integral equations on the real axis. The method's value stems from an explicit formula for the Cauchy integral of a complex exponential multiplied by a rational function.…
Finding the eigenvalues of a Sturm-Liouville problem can be a computationally challenging task, especially when a large set of eigenvalues is computed, or just when particularly large eigenvalues are sought. This is a consequence of the…
We introduce a technique for recovering a sufficiently smooth function from its ray transform over a wide class of curves in a general region of Euclidean space. The method is based on a complexification of the underlying vector fields…
This paper analyzes a method to approximate the first passage time probability density function which turns to be particularly useful if only sample data are available. The method relies on a Laguerre-Gamma polynomial approximation and…
In this paper, we propose a numerical method of computing an integral whose integrand is a slowly decaying oscillatory function. In the proposed method, we consider a complex analytic function in the upper-half complex plane, which is…
A concise overview of the spectral theory of integral-functional operators is provided. In the context of analysis, a technique is described for deriving solutions to equations involving operators in a closed form. A constructive theorem…
Q^2 evolution equations are important not only for describing hadron reactions in accelerator experiments but also for investigating ultrahigh-energy cosmic rays. The standard ones are called DGLAP evolution equations, which are…
We obtain wave functionals of free real and complex scalar fields on a 1+1 dimensional lattice by explicitly calculating the path integral for transition from one field configuration to another. The obtained expressions are useful for…
We investigate a numerical solution of the flavor-nonsinglet Altarelli-Parisi equation with next-to-leading-order $\alpha_s$ corrections by using Laguerre polynomials. Expanding a structure function (or a quark distribution) and a splitting…
We give an algorithm to compute inhomogeneous differential equations for definite integrals with parameters. The algorithm is based on the integration algorithm for $D$-modules by Oaku. Main tool in the algorithm is the Gr\"obner basis…
By means of a generalization of the Maurer-Cartan expansion method we construct a procedure to obtain expanded higher-order Lie algebras. The expanded higher order Maurer-Cartan equations for the case $\mathcal{G}=V_{0}\oplus V_{1}$ are…
Diffusive representations of fractional differential and integral operators can provide a convenient means to construct efficient numerical algorithms for their approximate evaluation. In the current literature, many different variants of…
This work deals with uncertainty quantification for a generic input distribution to some resource-intensive simulation, e.g., requiring the solution of a partial differential equation. While efficient numerical methods exist to compute…
We investigate a class of power series occurring in some problems in quantum optics. Their coefficients are either Gegenbauer or Laguerre polynomials multiplied by binomial coefficients. Although their sums have been known for a long time,…
We solve numerically the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equations for the evolution of fragmentation functions using the Laguerre method. We extend this method to include supersymmetric evolution. The solution to the…
An algorithm for solving the random resistor problem by means of the transfer-matrix approach is presented. Preconditioning by spanning clusters extraction both reduces the size of the conductivity matrix and speed up the calculations.
The first passage time problem is considered for stochastic logistic growth model with constant harvesting and multiplicative environmental noise. Explicit expressions for the moments and cumulants of both upcrossing and downcrossing FPTs…
We study evolution equations with non-self-adjoint generators, for example the convection-diffusion equation. Spectral expansions are not a reliable method of solving such equations, because they are so ill-conditioned. We introduce a new…