A NEW APPROACH TO FIND AN APPROXIMATE SOLUTION OF LINEAR INITIAL VALUE PROBLEMS WITH HIGH DEGREE OF ACCURACY

This work investigates a new approach to find closed form solution to linear initial value problems (IVP). Classical Bernoulli polynomials have been used to derive a finite set of orthonormal polynomials and a finite operational matrix to simplify derivatives in IVP. These orthonormal polynomials to...

Full description

Saved in:
Bibliographic Details
Published inTWMS journal of applied and engineering mathematics Vol. 12; no. 4; p. 1448
Main Author Singh, U. P
Format Journal Article
LanguageEnglish
Published Istanbul Turkic World Mathematical Society 01.01.2022
Elman Hasanoglu
Subjects
Accuracy
Approximation
Boundary value problems
Integral equations
Mathematical research
Ordinary differential equations
Partial differential equations
Polynomials
Robustness (mathematics)
India
Online AccessGet full text

Cover

More Information
Summary:This work investigates a new approach to find closed form solution to linear initial value problems (IVP). Classical Bernoulli polynomials have been used to derive a finite set of orthonormal polynomials and a finite operational matrix to simplify derivatives in IVP. These orthonormal polynomials together with the operational matrix of relevant order provides a robust approximation to the solution of a linear initial value problem by converting the IVP into a set of algebraic equations. Depending upon the nature of a problem, a polynomial of degree n or numerical approximation can be obtained. The technique has been demonstrated through four examples. In each example, obtained solution has been compared with available exact or numerical solution. High degree of accuracy has been observed in numerical values of solutions for considered problems. Keywords:approximate solution, Bernoulli polynomials, initial value problems, orthonormal polynomials. AMS Subject Classification: 34A45, B4B05, 11B68.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2146-1147
2146-1147