Solving System of Higher-Order Linear Differential Equations on the Level of Operators

Thota, Srinivasarao; Kumar, Shiv Datt

doi:10.12732/ijpam.v106i1.2

Cited by 6 publications

(3 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…with the initial conditions x 1 (0) = 1, x 1 (0) = 2, x 2 (0) = 0, x 2 (0) = −1, examined in [18]. The system matrix is…”

Section: Lemma 2 Given An Arbitrary Columnmentioning

confidence: 99%

Differential transcendence of solutions of systems of linear differential equations based on total reduction of the system

Jovovic¹

2020

APPL ANAL DISCRETE M

View full text Add to dashboard Cite

In this paper we consider total reduction of the nonhomogeneous linear system of operator equations with constant coefficients and commuting operators. The totally reduced system obtained in this manner is completely decoupled. All equations of the system differ only in the variables and in the nonhomogeneous terms. The homogeneous parts are obtained using the generalized characteristic polynomial of the system matrix. We also indicate how this technique may be used to examine differential transcendence of the solution of the linear system of the differential equations with constant coefficients over the complex field and meromorphic free terms.

show abstract

“…with the initial conditions x 1 (0) = 1, x 1 (0) = 2, x 2 (0) = 0, x 2 (0) = −1, examined in [18]. The system matrix is…”

Section: Lemma 2 Given An Arbitrary Columnmentioning

confidence: 99%

Differential transcendence of solutions of systems of linear differential equations based on total reduction of the system

Jovovic¹

2020

APPL ANAL DISCRETE M

View full text Add to dashboard Cite

show abstract

“…There are many other algorithms or methods for solving DAEs and also for differential equations available in the literature. [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] In this paper, we propose a general numerical method to solve the second-order system of DAEs using Adomian decomposition method (ADM). There are some general approaches methods available in the literature, 18,19,37,38 and these are developed for solving the first order DAEs.…”

Section: Introductionmentioning

confidence: 99%

On solving system of differential-algebraic equations using adomian decomposition method

Thota,

2023

F1000Res

View full text Add to dashboard Cite

Background: In this paper, we focus on an efficient and easy method for solving the given system of differential-algebraic equations (DAEs) of second order. Methods: The approximate solutions are computed rapidly and efficiently with the help of a semi-analytical method known as Adomian decomposition method (ADM). The logic of this method is simple and straightforward to understand. Results: To demonstrate the proposed method, we presented several examples and the computations are compared with the exact solutions to show the efficient. One can employ this logic to different mathematical software tools such as Maple, SCILab, Mathematica, NCAlgebra, Matlab etc. for the problems in real life applications. Conclusions: In this paper, we offered a method for solving the given system of secondorder nonlinear DAEs with aid of the ADM. We shown that the proposed method is simple and efficient, also one can obtain the approximate solutions quickly using this method. A couple of examples are discussed for illustrating this method and graphical and mathematical assessments are discussed with the analytical solutions of the given problems.

show abstract

“…(Thota and Kumar [ 1 , 2 , 5 , 7 , 9 ]) Let be an ordinary integro-differential algebra. Suppose is a monic scalar differential operator of order m and is fundamental system for T. Then the right inverse operator of T is given by where w is the determinant of the Wronskian matrix W for and the determinant of the matrix obtained from W by replacing the i - th column by m-th unit vector.…”

Section: Introductionmentioning

confidence: 99%

Initial value problems for system of differential-algebraic equations in Maple

Thota

2018

BMC Res Notes

View full text Add to dashboard Cite

show abstract

Solving System of Higher-Order Linear Differential Equations on the Level of Operators

Cited by 6 publications

References 9 publications

Differential transcendence of solutions of systems of linear differential equations based on total reduction of the system

Differential transcendence of solutions of systems of linear differential equations based on total reduction of the system

On solving system of differential-algebraic equations using adomian decomposition method

Initial value problems for system of differential-algebraic equations in Maple

Contact Info

Product

Resources

About