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 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 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 About the Dirichlet Boundary Value Problem using Clifford Algebras

2018 ◽  
Vol 15 ◽  
pp. 8098-8119
Author(s):  
Johan Ceballos
Keyword(s):  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Clifford Algebras ◽  
Dirichlet Boundary ◽  
Relevant Literature ◽  
Monogenic Functions ◽  
Dirichlet Boundary Value Problem ◽  
Dirichlet Problems ◽  
Initial Value ◽  
Do So

This paper reviews and summarizes the relevant literature on Dirichlet problems for monogenic functions on classic Clifford Algebras and the Clifford algebras depending on parameters on. Furthermore, our aim is to explore the properties when extending the problem to and, illustrating it using the concept of fibres. To do so, we explore ways in which the Dirichlet problem can be written in matrix form, using the elements of a Clifford's base. We introduce an algorithm for finding explicit expressions for monogenic functions for Dirichlet problems using matrices in Finally, we illustrate how to solve an initial value problem related to a fibre.

scholarly journals Existence of bounded solutions for fourth order Dirichlet problems with convex-concave nonlinearity

2009 ◽  
Vol 42 (1) ◽  
Author(s):  
Marek Galewski
Keyword(s):  
Boundary Value Problem ◽  
Growth Condition ◽  
Fourth Order ◽  
Dirichlet Boundary ◽  
Concave Function ◽  
Higher Order ◽  
Dirichlet Boundary Value Problem ◽  
Bounded Solutions ◽  
Dirichlet Problems ◽  
Concave Part

AbstractWe consider the Dirichlet boundary value problem for higher order O.D.E. with nonlinearity being the sum of a derivative of a convex and of a concave function in case when no growth condition is imposed on the concave part.

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