scholarly journals Biharmonic Problems with Polynomial Data in a Unit Sphere In $ R^3$

2018 ◽  
Author(s):  
Agah D. Garnadi ◽  
Ikhsan Maulidi
Keyword(s):  
Boundary Value Problem ◽  
Unit Sphere ◽  
Biharmonic Equation ◽  
Boundary Function ◽  
Exact Algorithms ◽  
Polynomial Functions ◽  
Dirichlet Problems ◽  
Simply Supported ◽  
Laplace Equations ◽  
Biharmonic Problems

We studied simply supported boundary value problem of Biharmonic equation. The problem is reformulated as a systems of Laplace-Poisson equation with Dirichlet problems. We utilize an exact algorithms for solving Laplace equations with Dirichlet conditions with polynomial functions data. The algorithm requires only differentiation of the boundary function, but no integration

scholarly journals Biharmonic Equation on Annulus in a Unit Sphere with Polynomial Boundary Condition

2017 ◽  
Vol 13 (1) ◽  
pp. 51
Author(s):  
Ikhsan Maulidi ◽  
Agah D Garnadi
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Unit Sphere ◽  
Biharmonic Equation ◽  
Boundary Value ◽  
Boundary Function ◽  
Exact Algorithms ◽  
Polynomial Functions ◽  
Dirichlet Conditions ◽  
Laplace Equations

We studied Biharmonic boundary value problem on annulus with polynomial data. We utilize an exact algorithms for solving Laplace equations with Dirichlet conditions with polynomial functions data. The algorithm requires differentiation of the boundary function, but no integration.

scholarly journals Biharmonic Equation on Annulus in a Unit Sphere with Polynomial Boundary Condition

2017 ◽  
Vol 13 (1) ◽  
pp. 51
Author(s):  
Ikhsan Maulidi ◽  
Agah D Garnadi
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Unit Sphere ◽  
Biharmonic Equation ◽  
Boundary Value ◽  
Boundary Function ◽  
Exact Algorithms ◽  
Polynomial Functions ◽  
Dirichlet Conditions ◽  
Laplace Equations

We studied Biharmonic boundary value problem on annulus with polynomial data. We utilize an exact algorithms for solving Laplace equations with Dirichlet conditions with polynomial functions data. The algorithm requires differentiation of the boundary function, but no integration.

scholarly journals Tri-Dirichlet-Type Problems with Polynomial Data in a Unit Sphere In $ R^3$

2017 ◽  
Author(s):  
Agah D. Garnadi
Keyword(s):  
Boundary Value Problem ◽  
Poisson Equation ◽  
Unit Sphere ◽  
Dirichlet Boundary ◽  
Boundary Function ◽  
Exact Algorithms ◽  
Polynomial Functions ◽  
Dirichlet Boundary Value Problem ◽  
Dirichlet Problems ◽  
Laplace Equations

We studied Tri-Dirichlet boundary value problem of TriLaplace equation. The problem is reformulated as a systems of Laplace-Poisson equation with Dirichlet problems. We utilize an exact algorithms for solving Laplace equations with Dirichlet conditions with polynomial functions data. The algorithm requires differentiation of the boundary function, but no integration.

scholarly journals Polyharmonic Problems with Simply Supported Polynomial Data in the Unit Ball in $ R^n$

2018 ◽  
Author(s):  
Agah D. Garnadi
Keyword(s):  
Boundary Value Problem ◽  
Unit Ball ◽  
Poisson Equation ◽  
Boundary Function ◽  
Exact Algorithms ◽  
Dirichlet Problems ◽  
Polyharmonic Equation ◽  
Dirichlet Conditions ◽  
Simply Supported ◽  
Laplace Equations

We studied simply supported polynomial data of boundary value problem of Polyharmonic equation. The problem is reformulated as a systems of Laplace-Poisson equation with Polynomial Dirichlet problems. We utilize an exact algorithms for solving Laplace equations with Dirichlet conditions with polynomial data. The algorithm requires differentiation of the boundary function, but no integration.

scholarly journals Simply Supported Biharmonic Equations with Polynomial Data in The Unit Ball of $ R^n$

2018 ◽  
Author(s):  
Agah D. Garnadi
Keyword(s):  
Unit Ball ◽  
Dirichlet Boundary ◽  
Exact Algorithms ◽  
Dirichlet Boundary Conditions ◽  
Polynomial Functions ◽  
Dirichlet Problems ◽  
Biharmonic Equations ◽  
Simply Supported ◽  
Poisson Equations ◽  
Laplace Equations

We studied simply supported boundary value problem of Biharmonic equation in the unit ball of $R^n, n \geq 3,$ with polynomial data. The problem is restated as a pair of Laplace and Poisson equations with polynomial Dirichlet problems. We utilize an exact algorithms for solving Laplace equations with Dirichlet boundary conditions with polynomial functions data. The algorithm requires only differentiation of the boundary data, but no integration

scholarly journals On Fast Solving Spectral Method to Biharmonic Equation Of the Second Kind

2018 ◽  
Author(s):  
Agah D. Garnadi
Keyword(s):  
Boundary Value Problem ◽  
Spectral Method ◽  
Biharmonic Equation ◽  
Boundary Value ◽  
Simply Supported

This note is addressed to fast solving simply supported boundary value problem ofbiharmonic equation in the unit rectangle.

scholarly journals On the discreteness of the spectra of the Dirichlet and Neumannp-biharmonic problems

2004 ◽  
Vol 2004 (9) ◽  
pp. 777-792 ◽  
Author(s):  
Jiří Benedikt
Keyword(s):  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Neumann Problem ◽  
Nonlinear Boundary ◽  
Neumann Boundary ◽  
Unbounded Sequence ◽  
The Neumann Problem ◽  
Biharmonic Problems ◽  
Zero Points

We are interested in a nonlinear boundary value problem for(|u″|p−2u″)′​′=λ|u|p−2uin[0,1],p>1, with Dirichlet and Neumann boundary conditions. We prove that eigenvalues of the Dirichlet problem are positive, simple, and isolated, and form an increasing unbounded sequence. An eigenfunction, corresponding to thenth eigenvalue, has preciselyn−1zero points in(0,1). Eigenvalues of the Neumann problem are nonnegative and isolated,0is an eigenvalue which is not simple, and the positive eigenvalues are simple and they form an increasing unbounded sequence. An eigenfunction, corresponding to thenth positive eigenvalue, has preciselyn+1zero points in(0,1).

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