The Experts below are selected from a list of 109896 Experts worldwide ranked by ideXlab platform
Tanaka Yoshitaro - One of the best experts on this subject based on the ideXlab platform.
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Method of fundamental solutions for Neumann problems of the modified Helmholtz equation in disk domains
'Elsevier BV', 2022Co-Authors: Ei Shin-ichiro, Ochiai Hiroyuki, Tanaka YoshitaroAbstract:The method of the fundamental solutions (MFS) is used to construct an approximate solution for a partial differential equation in a bounded domain. It is demonstrated by combining the fundamental solutions shifted to the points outside the domain and determining the coefficients of the linear sum to satisfy the boundary condition on the finite points of the boundary. In this paper, the existence of the approximate solution by the MFS for the Neumann problems of the modified Helmholtz equation in disk domains is rigorously demonstrated. We reveal the sufficient condition of the existence of the approximate solution. Applying the Green formula to the Neumann problem of the modified Helmholtz equation, we bound the error between the approximate solution and exact solution into the difference of the function of the boundary condition and the normal derivative of the approximate solution by boundary integrations. Using this estimate of the error, we show the convergence of the approximate solution by the MFS to the exact solution with Exponential Order, that is, N(2)a(N) Order, where a is a positive constant less than one and N is the number of collocation points. Furthermore, it is demonstrated that the error tends to 0 in Exponential Order in the numerical simulations with increasing number of collocation points N. (C) 2021 The Author(s). Published by Elsevier B.V
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Method of fundamental solutions for Neumann problems of the modified Helmholtz equation in disk domains
2020Co-Authors: Ei Shin-ichiro, Ochiai Hiroyuki, Tanaka YoshitaroAbstract:The method of the fundamental solutions (MFS) is used to construct an approximate solution for a partial differential equation in a bounded domain. It is demonstrated by combining the fundamental solutions shifted to the points outside the domain and determining the coefficients of the linear sum to satisfy the boundary condition on the finite points of the boundary. In this paper, the existence of the approximate solution by the MFS for the Neumann problems of the modified Helmholtz equation in disk domains is rigorously demonstrated. We reveal the sufficient condition of the existence of the approximate solution. Applying Green's theorem to the Neumann problem of the modified Helmholtz equation, we bound the error between the approximate solution and exact solution into the difference of the function of the boundary condition and the normal derivative of the approximate solution by boundary integrations. Using this estimate of the error, we show the convergence of the approximate solution by the MFS to the exact solution with Exponential Order, that is, $N^2a^N$ Order, where $a$ is a positive constant less than one and $N$ is the number of collocation points. Furthermore, it is demonstrated that the error tends to $0$ in Exponential Order in the numerical simulations with increasing number of collocation points $N$
Takashi Nanya - One of the best experts on this subject based on the ideXlab platform.
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control signal sharing using data path delay information at control data flow graph descriptions
Symposium on Asynchronous Circuits and Systems, 2003Co-Authors: Hiroshi Saito, Euiseok Kim, Nattha Sretasereekul, Masashi Imai, Hiroshi Nakamura, Takashi NanyaAbstract:Due to the state explosion problem, signal transition graph based asynchronous circuit synthesis cannot handle large specifications. To overcome this problem, we propose two control signal sharing methods by using the delay information of data-path circuit. Since the number of states is Exponential with the number of signals in the synthesis, the reduction of signals by sharing can reduce the number of states in Exponential Order. They are carried out at the control of data path operations which is represented as a control flow graph description, without sacrificing the critical path delay of the data-path circuit. Experimental results are encouraging in that a number of control signals can be shared by our methods.
Maha Yousef - One of the best experts on this subject based on the ideXlab platform.
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convergence of numerical schemes for the solution of partial integro differential equations used in heat transfer
Journal of Applied Mathematics and Computing, 2019Co-Authors: Kamel Alkhaled, Amer Darweesh, Maha YousefAbstract:Integro-differential equations play an important role in may physical phenomena. For instance, it appears in fields like fluid dynamics, biological models and chemical kinetics. One of the most important physical applications is the heat transfer in heterogeneous materials, where physician are looking for efficient methods to solve their modeled equations. The difficulty of solving integro-differential equations analytically made mathematician to search about efficient methods to find an approximate solution. The present article is designed to supply numerical solution of a parabolic Volterra integro-differential equation under initial and boundary conditions. We have made an attempt to develop a numerical solution via the use of Sinc-Galerkin method, the convergence analysis via the use of fixed point theory has been discussed, and showed to be of Exponential Order. For comparison purposes, we approximate the solution of integro-differential equation using Adomian decomposition method. Sometimes, the Adomian decomposition method is a highly efficient technique used to approximate analytical solution of differential equations, applicability of Adomian decomposition method to partial integro-differential equations has not been studied in details previously in the literatures. In addition, we present numerical examples and comparisons to support the validity of these proposed methods.
Ei Shin-ichiro - One of the best experts on this subject based on the ideXlab platform.
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Method of fundamental solutions for Neumann problems of the modified Helmholtz equation in disk domains
'Elsevier BV', 2022Co-Authors: Ei Shin-ichiro, Ochiai Hiroyuki, Tanaka YoshitaroAbstract:The method of the fundamental solutions (MFS) is used to construct an approximate solution for a partial differential equation in a bounded domain. It is demonstrated by combining the fundamental solutions shifted to the points outside the domain and determining the coefficients of the linear sum to satisfy the boundary condition on the finite points of the boundary. In this paper, the existence of the approximate solution by the MFS for the Neumann problems of the modified Helmholtz equation in disk domains is rigorously demonstrated. We reveal the sufficient condition of the existence of the approximate solution. Applying the Green formula to the Neumann problem of the modified Helmholtz equation, we bound the error between the approximate solution and exact solution into the difference of the function of the boundary condition and the normal derivative of the approximate solution by boundary integrations. Using this estimate of the error, we show the convergence of the approximate solution by the MFS to the exact solution with Exponential Order, that is, N(2)a(N) Order, where a is a positive constant less than one and N is the number of collocation points. Furthermore, it is demonstrated that the error tends to 0 in Exponential Order in the numerical simulations with increasing number of collocation points N. (C) 2021 The Author(s). Published by Elsevier B.V
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Method of fundamental solutions for Neumann problems of the modified Helmholtz equation in disk domains
2020Co-Authors: Ei Shin-ichiro, Ochiai Hiroyuki, Tanaka YoshitaroAbstract:The method of the fundamental solutions (MFS) is used to construct an approximate solution for a partial differential equation in a bounded domain. It is demonstrated by combining the fundamental solutions shifted to the points outside the domain and determining the coefficients of the linear sum to satisfy the boundary condition on the finite points of the boundary. In this paper, the existence of the approximate solution by the MFS for the Neumann problems of the modified Helmholtz equation in disk domains is rigorously demonstrated. We reveal the sufficient condition of the existence of the approximate solution. Applying Green's theorem to the Neumann problem of the modified Helmholtz equation, we bound the error between the approximate solution and exact solution into the difference of the function of the boundary condition and the normal derivative of the approximate solution by boundary integrations. Using this estimate of the error, we show the convergence of the approximate solution by the MFS to the exact solution with Exponential Order, that is, $N^2a^N$ Order, where $a$ is a positive constant less than one and $N$ is the number of collocation points. Furthermore, it is demonstrated that the error tends to $0$ in Exponential Order in the numerical simulations with increasing number of collocation points $N$
Hiroshi Saito - One of the best experts on this subject based on the ideXlab platform.
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control signal sharing using data path delay information at control data flow graph descriptions
Symposium on Asynchronous Circuits and Systems, 2003Co-Authors: Hiroshi Saito, Euiseok Kim, Nattha Sretasereekul, Masashi Imai, Hiroshi Nakamura, Takashi NanyaAbstract:Due to the state explosion problem, signal transition graph based asynchronous circuit synthesis cannot handle large specifications. To overcome this problem, we propose two control signal sharing methods by using the delay information of data-path circuit. Since the number of states is Exponential with the number of signals in the synthesis, the reduction of signals by sharing can reduce the number of states in Exponential Order. They are carried out at the control of data path operations which is represented as a control flow graph description, without sacrificing the critical path delay of the data-path circuit. Experimental results are encouraging in that a number of control signals can be shared by our methods.
