Solution of Cauchy Problem for Equation First Order Via Haar Functions

Lukomskii, D. S.; Lukomskii, S. F.; Терехин, П. А.

doi:10.18500/1816-9791-2016-16-2-151-159

Cited by 7 publications

(5 citation statements)

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“…is absolute continuous on the closed interval [0,1]. From this fact it immediately follows that (15) lim…”

Section: The Existence Of the Numerical Solutionmentioning

confidence: 84%

“…Algorithms of this kind are used frequently for solving differential equations numerically. Among them we would like to mention the method developed by Lukomskii and Terekhin in [15] to approximate the derivative of the solution by step functions for solving first order linear Cauchy problem with continuous coefficient and free term on the close interval [0, 1]. Our multistep algorithm only involves the integral means of these functions, so for us it is sufficient to suppose the continuity of them on the interval [0, 1[.…”

Section: Introductionmentioning

confidence: 99%

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Numerical solution of linear differential equations by Walsh polynomials approach

Gát

Toledo

2020

Studia Scientiarum Mathematicarum Hungarica

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In 1975 C. F. Chen and C. H. Hsiao established a new procedure to solve initial value problems of systems of linear differential equations with constant coefficients by Walsh polynomials approach. However, they did not deal with the analysis of the proposed numerical solution. In a previous article we study this procedure in case of one equation with the techniques that the theory of dyadic harmonic analysis provides us. In this paper we extend these results through the introduction of a new procedure to solve initial value problems of differential equations with not necessarily constant coefficients.

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“…is absolute continuous on the closed interval [0,1]. From this fact it immediately follows that (15) lim…”

Section: The Existence Of the Numerical Solutionmentioning

confidence: 84%

Section: Introductionmentioning

confidence: 99%

Numerical solution of linear differential equations by Walsh polynomials approach

Gát

Toledo

2020

Studia Scientiarum Mathematicarum Hungarica

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“…By applying the Haar functions [7], it is possible to receive a solution with a very small error, more accurate in some cases than the solution derived by the second order Runge-Kutta method. But the function must be superimposed with certain conditions.…”

Section: Construction Of Interpolation Methods For Numerical Solution mentioning

confidence: 99%

Construction of interpolation method for numerical solution of the Cauchy's problem

Bihun

Tsehelyk

2017

EEJET

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“…In [8], the authors present the derivative y of the solution y as a Haar expansion and obtain an estimate of the approximate solution in terms of the modulus of continuity of the coefficients p(x) and q(x). This method can also be used for equations with unbounded coefficients p(x) and q(x).…”

Section: Almost Everywhere On [A B]mentioning

confidence: 99%

Numerical solution of linear differential equations with discontinuous coefficients and Henstock integral

Lukomskii¹,

Lukomskii²

2020

Preprint

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In this article we consider the problem of approximative solution of linear differential equations y + p(x)y = q(x) with discontinuous coefficients p and q. We assume that coefficients of such equation are Henstock integrable functions. To find the approximative solution we change the original Cauchy problem to another problem with piecewise-constant coefficients. The sharp solution of this new problems is the approximative solution of the original Cauchy problem. We find the degree approximation in terms of modulus of continuity ω δ (P ), ω δ (Q), where P and Q are f -primitive for coefficients p and q.

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Solution of Cauchy Problem for Equation First Order Via Haar Functions

Cited by 7 publications

References 0 publications

Numerical solution of linear differential equations by Walsh polynomials approach

Numerical solution of linear differential equations by Walsh polynomials approach

Construction of interpolation method for numerical solution of the Cauchy's problem

Numerical solution of linear differential equations with discontinuous coefficients and Henstock integral

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