scholarly journals Pell-Lucas collocation method to solve high-order linear Fredholm-Volterraintegro-differential equations and residual correction

2020 ◽  
Vol 44 (4) ◽  
pp. 1065-1091
Author(s):  
Şuayip YÜZBAŞI ◽  
Gamze YILDIRIM
Keyword(s):  
Differential Equations ◽  
Collocation Method ◽  
High Order ◽  
Order Linear ◽  
Residual Correction

A Numerical Approach for Solving High-Order Linear Delay Volterra Integro-Differential Equations

2018 ◽  
Vol 15 (05) ◽  
pp. 1850042 ◽  
Author(s):  
Şuayip Yüzbaşı ◽  
Murat Karaçayır
Keyword(s):  
Differential Equations ◽  
Approximate Solutions ◽  
Equation System ◽  
Numerical Approach ◽  
High Order ◽  
Inner Product ◽  
Present Scheme ◽  
Order Linear ◽  
Linear Delay ◽  
Residual Correction

In this study, a numerical method is proposed to solve high-order linear Volterra delay integro-differential equations. In this approach, we assume that the exact solution can be expressed as a power series, which we truncate after the [Formula: see text]-st term so that it becomes a polynomial of degree [Formula: see text]. Substituting the unknown function, its derivatives and the integrals by their matrix counterparts, we obtain a vector equivalent of the equation in question. Applying inner product to this vector with a set of monomials, we are left with a linear algebraic equation system of [Formula: see text] unknowns. The approximate solution of the problem is then computed from the solution of the resulting linear system. In addition, the technique of residual correction, whose aim is to increase the accuracy of the approximate solutions by estimating the error of those solutions, is discussed briefly. Both the method and this technique are illustrated with several examples. Finally, comparison of the present scheme with other methods is made wherever possible.

Solving systems of high-order linear ordinary differential equations with variable coefficients by means of exponential Chebyshev collocation method

2017 ◽  
Vol 8 (1-2) ◽  
pp. 40 ◽  
Author(s):  
Mohamed Ramadan ◽  
Kamal Raslan ◽  
Talaat El Danaf ◽  
Mohamed A. Abd Elsalam
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Collocation Method ◽  
Variable Coefficients ◽  
High Order ◽  
Matrix Equations ◽  
Algebraic Equations ◽  
Order Linear ◽  
Linear Ordinary Differential Equations ◽  
Linear Algebraic Equations

The purpose of this paper is to investigate the use of exponential Chebyshev (EC) collocation method for solving systems of high-order linear ordinary differential equations with variable coefficients with new scheme, using the EC collocation method in unbounded domains. The EC functions approach deals directly with infinite boundaries without singularities. The method transforms the system of differential equations and the given conditions to block matrix equations with unknown EC coefficients. By means of the obtained matrix equations, a new system of equations which corresponds to the system of linear algebraic equations is gained. Numerical examples are given to illustrative the validity and applicability of the method.

scholarly journals On Conjugacy of High-Order Linear Ordinary Differential Equations

1994 ◽  
Vol 1 (1) ◽  
pp. 1-8
Author(s):  
T. Chanturia
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
High Order ◽  
Summable Function ◽  
Order Linear ◽  
Linear Ordinary Differential Equations

Abstract It is shown that the differential equation u (n) = p(t)u, where n ≥ 2 and p : [a, b] → ℝ is a summable function, is not conjugate in the segment [a, b], if for some l ∈ {1, . . . , n – 1}, α ∈]a, b[ and β ∈]α, b[ the inequalities hold.

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