One of the well-known schemes for the direct numerical integration of second-order initial-value problems is due to Falkner. This paper focuses on the construction of a family of adapted block Falkner methods which are frequency dependent for the dir...
We consider a two-step numerical approach for solving parabolic initial boundary value problems in 3D simply connected smooth regions. The method uses the Laplace transform in time, reducing the problem to a set of independent stationary boundary val...
There are dozens of block methods in literature intended for solving second order initial-value problems. This article aimed at the analysis of the efficiency of k-step block methods for directly solving general second-order initial-value problems. E...
In this paper, we study an inverse problem to identify the initial value problem of the homogeneous Rayleigh–Stokes equation for a generalized second-grade fluid with the Riemann–Liouville fractional derivative model. This problem is ill posed; that...
In this paper, we present an accurate numerical approach based on the reproducing kernel method (RKM) for solving second-order fuzzy initial value problems (FIVP) with symmetry coefficients such as symmetric triangles and symmetric trapezoids. Findin...
The present manuscript examines different forms of Initial-Value Problems (IVPs) featuring various types of Ordinary Differential Equations (ODEs) by proposing a proficient modification to the famous standard Adomian decomposition method (ADM). The p...
A 5(4) pair of embedded explicit trigonometrically-fitted Runge–Kutta–Nyström (EETFRKN) methods especially designed for the numerical integration of second order initial value problems with oscillatory solutions is presented in this paper. Algebraic...
In this study, we construct new numerical methods for solving the initial value problem (IVP) in ordinary differential equations based on a symmetrical quadrature integration formula using hybrid functions. The proposed methods are designed to provid...
This study presents a new variant of the hybrid block methods (HBMs) for solving initial value problems (IVPs). The overlapping hybrid block technique is developed by changing each integrating block of the HBM to incorporate the penultimate intra-ste...
To solve the difficult problem of selecting initial guess values for component-level aero-engine start-up models, a novel method based on the flow-based back-calculation algorithm (FBBCA) is investigated. By exploiting the monotonic feature of low-sp...
In the essay, we consider an initial value question for a mixed initial-boundary value of time-fractional diffusion-wave equations. This matter is an ill-posed problem; the solution relies discontinuously on the measured information. The truncation r...
In this work, we introduce an efficient scheme for the numerical solution of some Boundary and Initial Value Problems (BVPs-IVPs). By using an operational matrix, which was obtained from the first kind of Chebyshev polynomials, we construct the algeb...
Sobolev’s initial value method is used to solve the Hammerstain equation of the second kind.
Recently, the author developed a theory for the computation of the phase lag and amplification factor for explicit and implicit multistep methods for first-order differential equations. In this paper, we will investigate the role of the derivatives o...
Chaos theory has applications in several disciplines and is focusing on the behavior of dynamical systems that are highly sensitive to initial conditions. Chaotic dynamics are the impromptu behavior displayed by some nonlinear dynamical frameworks an...
International oil and gas companies listed in New York must publish the information of oil and gas reserves under the SEC (United States Securities and Exchange Commission) standards every year. For greatly improving the SEC reserve, the SEC reserve...
The author has just published a theory on first-order differential equations that accounts for the phase-lag and amplification-factor calculations using explicit, implicit, and backward differentiation multistep methods. Eliminating the phase-lag and...
In this paper, we develop an explicit symmetric six-step method for the numerical solution of second-order initial value problems (IVPs) with oscillating solutions. The proposed method is phase-fitted and incorporates a free coefficient as a paramete...
For the purpose of solving a second-order singularly perturbed problem (SPP) with variable coefficients, a mth-order asymptotic-numerical method was developed, which decomposes the solutions into two independent sub-problems: a reduced first-order li...
The initial boundary-value problem associated to a semilinear wave equation with time-dependent boundary values was approximated by using the method of lines. Time integration is achieved by means of an explicit time method obtained from an arbitrari...
In this paper, the inverse problems for the boundary value and initial value in a heat equation are posed and solved. It is well known that those problems are ill posed. The problems are reformulated as integral equations of the first kind by using t...
A nonlinear transformation from the solution of linear KdV equation to the solution of Sharma-Tasso-Olver (STO) equation is derived out by using simplified homogeneous balance (SHB) method. According to the nonlinear transformation derived here, the...
This article presents an innovative approximating technique for addressing modified anomalous time-fractional sub-diffusion equations (MAFSDEs) of the Caputo type. These equations generalize classical diffusion equations, which involve fractional der...
A boundary-initial value problem for a fractional partial differential equation with sequential Caputo derivatives is studied. Exact analytical solutions are derived via the Fourier sine spectral method, with time-dependent coefficients expressed in...
The class of A-stable symmetric one-step Hermite–Obreshkov (HO) methods introduced by F. Loscalzo in 1968 for dealing with initial value problems is analyzed. Such schemes have the peculiarity of admitting a multiple knot spline extension collocating...
Numerical methods for the solution of ordinary differential equations are based on polynomial interpolation. In 1952, Brock and Murray have suggested exponentials for the case that the solution is known to be of exponential type. In 1961, Gautschi ca...
This article introduces a computational hybrid one-step technique designed for solving initial value differential systems of a first order, which utilizes second derivative function evaluations. The method incorporates three intra-step symmetric poin...
Absolute value problems of the form
This research introduces a fresh methodology for creating efficient numerical algorithms to solve first-order Initial Value Problems (IVPs). The study delves into the theoretical foundations of these methods and demonstrates their application to the...
Using an integral method based on indefinite integrals
In this work, a new pair of diagonally implicit Runge–Kutta–Nyström methods with four stages is constructed. The proposed method has been derived to solve initial value problems of special second-order ordinary-differential equations...
In this article, we present a numerical iterative scheme for solving a non-local singular initial-boundary value problem by combining two well known efficient methods. Namely, the homotopy analysis method and the double Laplace transform method. The...
In this article, the coupled Kundu equations are analyzed using the Fokas unified method on the half-line. We resolve a Riemann–Hilbert (RH) problem in order to illustrate the representation of the potential function in the coupled Kundu equati...
This research presents innovative modified explicit block methods with fifth-order algebraic accuracy to address initial value problems (IVPs). The derivation of the methods employs fitting coefficients that eliminate phase lag and amplification erro...
In this paper, we study the existence of extremal solutions for a Caputo-type fractional-order initial value problem. By using the monotone iteration technique and the upper–lower solution method, we obtain our existence theorem when the nonlin...
In this paper, we propose a new numerical scheme based on a variation of the standard formulation of the Runge–Kutta method using Taylor series expansion for solving initial value problems (IVPs) in ordinary differential equations. Analytically...
In the present note, a new modification of the Adomian decomposition method is developed for the solution of fractional-order diffusion-wave equations with initial and boundary value Problems. The derivatives are described in the Caputo sense. The ge...
This study introduces a family of implicit four-point block methods for solving first-order initial value problems (IVPs) with oscillatory solutions. In addition to an eighth-order block method, amplification-fitted and phase-fitted implicit block me...
The Fokas method exhibits remarkable versatility in solving boundary value problems associated with both linear and nonlinear partial differential equations, particularly when conventional approaches encounter challenges in handling intricate boundar...
In this study, the slope deflection method was presented for structures made of small-scaled axially functionally graded beams with a variable cross section within the scope of nonlocal elasticity theory. The small-scale effect between individual ato...
This paper presents a new hybrid block method formulated in variable stepsize mode to solve some first-order initial value problems of ODEs and time-dependent partial differential equations in applied sciences and engineering. The proposed method is...
We consider the scalar autonomous initial value problem as solved by an explicit Runge–Kutta pair of orders 6 and 5. We focus on an efficient family of such pairs, which were studied extensively in previous decades. This family comes with 5 coefficie...
22 June 2018
Americans fill upward of four billion prescriptions for pharmaceuticals each year, and many of those pharmaceuticals eventually make their way into the environment. Hundreds of different active pharmaceutical ingredients (APIs) are detected in ambien...
The present paper deals with neural algorithms to learn the singular value decomposition (SVD) of data matrices. The neural algorithms utilized in the present research endeavor were developed by Helmke and Moore (HM) and appear under the form of two...
The benefits and properties of iterative splitting methods, which are based on serial versions, have been studied in recent years, this work, we extend the iterative splitting methods to novel classes of parallel versions to solve nonlinear fractiona...
In this paper we apply extrapolation to increase the accuracy of approximations to the solution of the fuzzy initial value problems, based on the standard Euler method and Midpoint method, [11]. The method in detail is discussed and is illustrated by...
The authors of the above mentioned paper specify that the considered class of one-step symmetric Hermite-Obreshkov methods satisfies the property of conjugate-symplecticity up to order
We propose a new method of adaptive piecewise approximation based on Sinc points for ordinary differential equations. The adaptive method is a piecewise collocation method which utilizes Poly-Sinc interpolation to reach a preset level of accuracy for...
As an underground metal detection technology, the electromagnetic induction (EMI) method is widely used in many cases. Therefore, the EMI detection algorithms with excellent performance are worth studying. One of the EMI detection methods in the unde...
In this research, we provide a novel approach to the development of effective numerical algorithms for the solution of first-order IVPs. In particular, we detail the fundamental theory behind the development of the aforementioned approaches and show...
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