General analytical solution for the one dimensional regular Cauchy problem of Euler-Poisson-Darboux equation

Kweyu, David; Manyonge, A. W.

doi:10.12988/ams.2017.7133

ams

2017

DOI: 10.12988/ams.2017.7133

|View full text |Cite

General analytical solution for the one dimensional regular Cauchy problem of Euler-Poisson-Darboux equation

David Kweyu¹,

A. W. Manyonge²

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2017

2021

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

Exact solution of Singular Cauchy problem for Euler-Poisson-Darboux equation

John

2021

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

In this work we studied Lie group symmetry of non-linear ordinary differential equations and partial differential equations. And we tried solve a singular Cauchy problem for Euler-Poisson-Darboux equation by use this method because we want to found exact solution. Lie group symmetry takes exact solution if and only if any equation is invariant. When we applied lie group symmetry on a singular Cauchy problem for Euler-Poisson-Darboux equation we have got a polynomial of equations and we equal this polynomial for zero, after that we got many equations equal to zero, when we solve those equations we can’t found infinitesimal transformation of a singular Cauchy problem for Euler-Poisson-Darboux equation. And for this reason, we raised the order of the derivative to a higher level, we also derived a new generator corresponding to the order of the new equation. When we solve new equation we can find infinitesimal transformation of these equations by many method of Mathematics, and by used algorithm of Lie group Symmetries, we got general solution of singular Cauchy problem for Euler-Poisson-Darboux equation.

show abstract

Exact solution of Singular Cauchy problem for Euler-Poisson-Darboux equation

John

2021

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

show abstract

On the solution of n-dimensional regular Cauchy problem of Euler-Poisson-Darboux equation (EPD)

Kweyu¹,

Manyonge²

2017

ams

View full text Add to dashboard Cite

A general exact solution to the n-dimensional regular Cauchy problem of Euler-Poisson-Darboux (EPD) equation has been studied. Firstly, the general exact solution for the one dimensional regular Cauchy problem of EPD has been worked out. The EPD which is a second order Partial Differential Equation (PDE) is converted into an Ordinary Differential Equation (ODE) by method of separation of variables. On solving the ODE, the first complementary function (cf) is obtained directly. The second cf is obtained when the first derivative is eliminated from the ODE and then the ODE solved. When the expression for eliminating the first derivative is solved, a third term is obtained. The general solution for the one dimensional regular Cauchy EPD is therefore the product of the three terms. The procedure has been repeated for the two dimensional and n-dimensional cases. The general solutions for these cases are products of four terms and n+2 terms respectively. Finally, the general exact solution for n-dimensional regular Cauchy wave equation when k = 0, has also been obtained.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

General analytical solution for the one dimensional regular Cauchy problem of Euler-Poisson-Darboux equation

Cited by 2 publications

References 1 publication

Exact solution of Singular Cauchy problem for Euler-Poisson-Darboux equation

Exact solution of Singular Cauchy problem for Euler-Poisson-Darboux equation

On the solution of n-dimensional regular Cauchy problem of Euler-Poisson-Darboux equation (EPD)

Contact Info

Product

Resources

About