Related papers: The method of solving a scalar initial value probl…
Two important cases, where boundary conditions and solutions of the well-known integrable equations on a semi-strip are uniquely determined by the initial conditions, are rigorously studied in detail. First, the case of rectangular matrix…
Optimal prediction (OP) methods compensate for a lack of resolution in the numerical solution of complex problems through the use of an invariant measure as a prior measure in the Bayesian sense. In first-order OP, unresolved information is…
A high precision, and space time fully decoupled, wavelet formulation numerical method is developed for a class of nonlinear initial boundary value problems. This method is established based on a proposed Coiflet based approximation scheme…
This paper investigates a class of non-autonomous highly oscillatory ordinary differential equations characterized by a linear component inversely proportional to a small parameter $\varepsilon$, with purely imaginary eigenvalues, and an…
A step-search sequential quadratic programming method is proposed for solving nonlinear equality constrained stochastic optimization problems. It is assumed that constraint function values and derivatives are available, but only stochastic…
The automatic selection of an appropriate time step size has been considered extensively in the literature. However, most of the strategies developed operate under the assumption that the computational cost (per time step) is independent of…
We consider initial value problems for differential-algebraic equations in a possibly infinite-dimensional Hilbert space. Assuming a growth condition for the associated operator pencil, we prove existence and uniqueness of solutions for…
This article introduces a pedagogical method for {\it solving combinatorial problems} that frequently involve structures that are unfamiliar or less familiar. Indeed, an indirect method has been proposed in order to evade any possible…
Direct solution of simultaneous linear equations is regarded to be slow for large systems of equations and requires special treatment to avoid numerical instability. A new method is proposed that addresses the numerical instability without…
In this paper we apply a scaling invariance analysis to reduce a class of parabolic moving boundary problems to free boundary problems governed by ordinary differential equations. As well known free boundary problems are always non-linear…
In this paper, we introduce an iterative numerical method to solve systems of nonlinear equations. The third-order convergence of this method is analyzed. Several examples are given to illustrate the efficiency of the proposed method.
The phase-integral method (PIM) is an asymptotic method of the geometrical optics or semi-classical type for solving approximately, but in many cases very accurately, a wide class of differential equations in physics. Unlike the related…
We propose the numerical methods for solution of the weakly regular linear and nonlinear evolutionary (Volterra) integral equation of the first kind. The kernels of such equations have jump discontinuities along the continuous curves…
The paper focuses on solving one class of Volterra equations of the first kind, which is characterized by the variability of all integration limits. These equations were introduced in connection with the problem of identifying nonsymmetric…
Further development of the method of computational experiments for solving ill-posed problems is given. The effective (unoverstated) estimate for solution error of the first-kind equation is obtained using the truncating singular numbers…
The numerical simulation of the 3D incompressible Euler equation is analyzed with respect to different integration methods. The numerical schemes we considered include spectral methods with different strategies for dealiasing and two…
Some more general "inheritance conditions" have been found for a given set of symmetry generators $\{\mathbf{Z}_{\bar{l}}\}$ acting on some set of coupled ordinary differential equations, once the "first integration method" has been applied…
This paper focuses on the numerical solution of initial value problems for fractional differential equations of linear type. The approach we propose grounds on expressing the solution in terms of some integral weighted by a generalized…
We study a numerical approximation for a nonlinear variable-order fractional differential equation via an integral equation method. Due to the lack of the monotonicity of the discretization coefficients of the variable-order fractional…
Different possible sources are discussed for enhancement of the calculation time when solving ordinary differential equations systems to forecast space objects' motion. This paper presents an approach for building an integrator of ordinary…