scholarly journals Summability of formal solutions for a family of generalized moment integro-differential equations

2021 ◽  
Vol 24 (5) ◽  
pp. 1445-1476
Author(s):  
Alberto Lastra ◽  
Sławomir Michalik ◽  
Maria Suwińska
Keyword(s):  
Differential Equations ◽  
Variable Coefficients ◽  
Time Variable ◽  
High Interest ◽  
The Moment ◽  
Formal Solutions ◽  
Derivatives Of ◽  
Generalized Moment

Abstract Generalized summability results are obtained regarding formal solutions of certain families of linear moment integro-differential equations with time variable coefficients. The main result leans on the knowledg e of the behavior of the moment derivatives of the elements involved in the problem. A refinement of the main result is also provided giving rise to more accurate results which remain valid in wide families of problems of high interest in practice, such as fractional integro-differential equations.

Series Solutions for Beams on Elastic Foundations

1971 ◽  
Vol 38 (2) ◽  
pp. 507-514 ◽  
Author(s):  
M. Hete´nyi
Keyword(s):  
Differential Equations ◽  
Loading Conditions ◽  
Series Solutions ◽  
Sine Series ◽  
Hyperbolic Functions ◽  
Elastic Line ◽  
Beams On Elastic Foundation ◽  
Hinged Beams ◽  
Formal Solutions ◽  
Derivatives Of

In this paper series solutions are derived for beams on elastic foundation, subjected to a variety of end and loading conditions. These series solutions have the following advantages over the “formal” solutions of the differential equations of the corresponding problems: 1. The parameters of the beams (EI and l) and the modulus of the foundation (k) appear in these formulas in an explicit form and are not incorporated in the arguments of trigonometric and hyperbolic functions, as it is in the case of the formal solutions of the corresponding differential equations. For this reason, the series formulas are very suitable for design purposes and can also be used to obtain any desired degree of accuracy. 2. These formulas are valid for the entire lengths of the beams, irrespective of the discontinuities in the derivatives of the elastic line caused by the loadings. Solutions, for hinged-hinged beams, which reduce to the form of simple sine series, are not discussed here because they can be found in the related literature in a large variety of loading conditions.

A new exponential Chebyshev operational matrix of derivatives for solving high-order ordinary differential equations in unbounded domains

2016 ◽  
Vol 7 (1) ◽  
pp. 19 ◽  
Author(s):  
Mohamed Ramadan ◽  
Kamal Raslan ◽  
Talaat El Danaf ◽  
Mohamed A. Abd Elsalam
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Collocation Method ◽  
Operational Matrix ◽  
Variable Coefficients ◽  
High Order ◽  
Algebraic Equations ◽  
Linear Ordinary Differential Equations ◽  
The Given ◽  
Derivatives Of

The purpose of this paper is to investigate a new exponential Chebyshev (EC) operational matrix of derivatives. The new operational matrix of derivatives of the EC functions is derived and introduced for solving high-order linear ordinary differential equations with variable coefficients in unbounded domain using the collocation method. This method transforms the given differential equation and conditions to matrix equation with unknown EC coefficients. These matrices together with the collocation method are utilized to reduce the solution of high-order ordinary differential equations to the solution of a system of algebraic equations. The solution is obtained in terms of EC functions. Numerical examples are given to demonstrate the validity and applicability of the method. The obtained numerical results are compared with others existing methods and the exact solution where it shown to be very attractive with good accuracy.

scholarly journals On Adomian decomposition method for solving nonlinear ordinary differential equations of variable coefficients

2020 ◽  
Vol 4 (1) ◽  
pp. 476-484
Author(s):  
AbdulAzeez Kayode Jimoh ◽  
◽  
Aolat Olabisi Oyedeji ◽  
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Decomposition Method ◽  
Numerical Solutions ◽  
Adomian Decomposition Method ◽  
Variable Coefficients ◽  
Nonlinear Ordinary Differential Equations ◽  
Adomian Decomposition ◽  
Constant Coefficients ◽  
Derivatives Of

This paper considers the extension of the Adomian decomposition method (ADM) for solving nonlinear ordinary differential equations of constant coefficients to those equations with variable coefficients. The total derivatives of the nonlinear functions involved in the problem considered were derived in order to obtain the Adomian polynomials for the problems. Numerical experiments show that Adomian decomposition method can be extended as alternative way for finding numerical solutions to ordinary differential equations of variable coefficients. Furthermore, the method is easy with no assumption and it produces accurate results when compared with other methods in literature.

A Computer-Simulated Method of Phase-Plane Displacements

1970 ◽  
Vol 92 (2) ◽  
pp. 233-237 ◽  
Author(s):  
Louis L. Scharf
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Phase Plane ◽  
Nonlinear Differential Equations ◽  
Variable Coefficients ◽  
Time Variable ◽  
Second Order Differential Equations ◽  
Simple Set ◽  
Linear And Nonlinear ◽  
Plane Technique

A well-known graphical phase-plane technique for solving a wide variety of ordinary second-order differential equations is shown to satisfy a relatively simple set of iterative relationships which are easily programmed on a digital computer. The only restriction on the differential equation of interest is that it can be written as ax¨ + G(x, x˙, t) = 0, where G(x, x˙, t) = g(x, x˙, t) + kx. Consequently, many linear and nonlinear differential equations, with or without forcing functions, which may also have (explicit) time-variable coefficients, are easily solved with the method.

Sistem Pendukung Keputusan Pemilihan Taksi Berbasis Web dengan Algoritma Pencarian Linear

2016 ◽  
Vol 7 (2) ◽  
pp. 148-154
Author(s):  
Bimo Satriantoro ◽  
Ni Made Satvika Iswari
Keyword(s):  
Public Transportation ◽  
Time Variable ◽  
Variable Speed ◽  
Linear Algorithm ◽  
High Interest ◽  
Distance Variable ◽  
Google Apps

Indonesian people have a high interest for public transportation. There are few kind of public transportation, and taxi is one of them. Taxi use taximeter to calculate passanger fares. Taximeters between taxi companies are different in term of results although using the same equation and principle. The total fare from the taximeter is based on equation that includes distance variable, speed of the vehicle, and time variable. People have a problem to choose taxi because of the differnces of taximeter fares and taxi pool. Based on the problem, the solution is an application to help customer to decide choosing taxi. The application will help customer by giving informations about taximeter and carpool form two different company. The informations are based on the distance of the start point and the finish point of the customer and based on the distances of the customer and the carpool of the taxy company that will processed trough the application to calculating the total fares for the customer between two taxi companies. By using algorithm for linear searching, customer will get the informations to help them to decide which taxi the customer will use. Keywords: Linear Algorithm, Taximeter, Google Apps, Choice, Taxi

MODELING OF NONLINEAR VIBRATION PROBLEMS WITH FLUID FLOWS THROUGH PIPELINES

2018 ◽  
pp. 44-47
Author(s):  
F.J. Тurayev
Keyword(s):  
Differential Equations ◽  
Nonlinear Vibration ◽  
Viscoelastic Properties ◽  
Construction Material ◽  
Fluid Flows ◽  
Variable Coefficients ◽  
Algebraic Equations ◽  
Flowing Liquid ◽  
Vibration Problems

In this paper, mathematical model of nonlinear vibration problems with fluid flows through pipelines have been developed. Using the Bubnov–Galerkin method for the boundary conditions, the resulting nonlinear integro-differential equations with partial derivatives are reduced to solving systems of nonlinear ordinary integro-differential equations with both constant and variable coefficients as functions of time.A system of algebraic equations is obtained according to numerical method for the unknowns. The influence of the singularity of heredity kernels on the vibrations of structures possessing viscoelastic properties is numerically investigated.It was found that the determination of the effect of viscoelastic properties of the construction material on vibrations of the pipeline with a flowing liquid requires applying weakly singular hereditary kernels with an Abel type singularity.

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