Operational Matrices from a Frame and their Applications in Solving Boundary Value Problems with Mixed Boundary Conditions

2018 ◽  
Vol 4 (5) ◽  
Author(s):  
Mahendra Kumar Jena ◽  
Kshama Sagar Sahu
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Mixed Boundary Conditions ◽  
Operational Matrices

Three-Dimensional Boundary Value Problems of Elastothermodiffusion with Mixed Boundary Conditions

1997 ◽  
Vol 4 (3) ◽  
pp. 243-258
Author(s):  
T. Burchuladze ◽  
Yu. Bezhuashvili
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Singular Integrals ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Three Dimensional ◽  
Boundary Surface ◽  
Mixed Boundary Conditions ◽  
Theory Of Elasticity ◽  
Classical Solutions

Abstract We investigate the basic boundary value problems of the connected theory of elastothermodiffusion for three-dimensional domains bounded by several closed surfaces when the same boundary conditions are fulfilled on every separate boundary surface, but these conditions differ on different groups of surfaces. Using the results of papers [Kupradze, Gegelia, Basheleishvili, and Burchuladze, Three-dimensional problems of the mathematical theory of elasticity and thermoelasticity, North-Holland Publishing Company, 1979, Russian original, 1976–Mikhlin, Multi-dimensional singular integrals and integral equations, 1962], we prove theorems on the existence and uniqueness of the classical solutions of these problems.

scholarly journals Numerical Results for Linear Sequential Caputo Fractional Boundary Value Problems

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 910
Author(s):  
Bhuvaneswari Sambandham ◽  
Aghalaya S. Vatsala ◽  
Vinodh K. Chellamuthu
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Mixed Boundary Conditions ◽  
Numerical Code ◽  
Fractional Boundary Value Problem ◽  
Monotone Method ◽  
Fractional Boundary Value Problems

The generalized monotone iterative technique for sequential 2 q order Caputo fractional boundary value problems, which is sequential of order q, with mixed boundary conditions have been developed in our earlier paper. We used Green’s function representation form to obtain the linear iterates as well as the existence of the solution of the nonlinear problem. In this work, the numerical simulations for a linear nonhomogeneous sequential Caputo fractional boundary value problem for a few specific nonhomogeneous terms with mixed boundary conditions have been developed. This in turn will be used as a tool to develop the accurate numerical code for the linear nonhomogeneous sequential Caputo fractional boundary value problem for any nonhomogeneous terms with mixed boundary conditions. This numerical result will be essential to solving a nonlinear sequential boundary value problem, which arises from applications of the generalized monotone method.

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