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A Third-Order P-Laplacian Boundary Value Problem On An Unbounded Domain, Samuel Azubuike Iyase, Ogbu Famous Imaga
A Third-Order P-Laplacian Boundary Value Problem On An Unbounded Domain, Samuel Azubuike Iyase, Ogbu Famous Imaga
Turkish Journal of Mathematics
In this work, we apply Leray-Schauder continuation principle to establish the existence of at least one solution to the third order p-Laplacian boundary value problem on an unbounded domain of the form \begin{equation*} (w(t) \varphi_{p}( u^{\prime\prime}(t)))^{\prime} = K ( t, u(t) , u^{\prime}(t), u^{\prime\prime}(t) ) , t \in ( 0, \infty) \end{equation*} \begin{equation*} u(0)= 0, \, u^{\prime} (0) = \sum^{m}_{i=1} \alpha _{i} \int_{0}^{\xi_{i}} u(t) dt, \, \lim_{t \rightarrow\infty} ( w(t)\varphi_{p} ( u^{\prime \prime} (t)) = 0 \end{equation*} under the nonresonant condition $ \sum_{i=1}^{m} \alpha_{i} \xi^{2} \neq 2. $
A Performance Assessment Of An Hdg Method For Second-Order Fredholm Integro-Differential Equation: Existence-Uniqueness And Approximation, Mehmet Fati̇h Karaaslan
A Performance Assessment Of An Hdg Method For Second-Order Fredholm Integro-Differential Equation: Existence-Uniqueness And Approximation, Mehmet Fati̇h Karaaslan
Turkish Journal of Mathematics
In this paper, we obtain the existence--uniqueness of solution to the second-order linear Fredholm integro-differential equation (FIDE) with Dirichlet boundary condition by hybridizable discontinuous Galerkin (HDG) method. A key property of these methods is to eliminate all internal degrees of freedom and to construct a linear system that only includes globally coupled unknowns at the element interfaces. After designing and implementing HDG algorithm, we provide some necessary and sufficient conditions based on the stabilization parameter and kernel function to guarantee the existence-uniqueness of the approximate solution. Then, some numerical examples are carried out to assess the performance of the present …
A New Implicit-Explicit Local Differential Method For Boundary Value Problems, Hüseyi̇n Tunç, Murat Sari
A New Implicit-Explicit Local Differential Method For Boundary Value Problems, Hüseyi̇n Tunç, Murat Sari
Turkish Journal of Mathematics
In this study, an effective numerical method based on Taylor expansions is presented for boundary value problems. This method is arbitrary directional and called as implicit-explicit local differential transform method (IELDTM). With the completion of this study, a reliable numerical method is derived by optimizing the required degrees of freedom. It is shown that the order refinement procedure of the IELDTM does not affect the degrees of freedom. A priori error analysis of the current method is constructed and order conditions are presented in a detailed analysis. The theoretical order expectations are verified for nonlinear BVPs. Stability of the IELDTM …