This paper proposes a numerical method to the two-dimensional hyperbolic equations with nonlocal integral conditions. The nonlocal integral equation is of major challenge in the frame work of the numerical solutions of PDEs. The method benefits from collocation radial b More
This paper proposes a numerical method to the two-dimensional hyperbolic equations with nonlocal integral conditions. The nonlocal integral equation is of major challenge in the frame work of the numerical solutions of PDEs. The method benefits from collocation radial basis function method, the generalized thin plate splines radial basis functions are used.Therefore, it does not require any struggle to determine shape parameter (In other RBFs, it is time-consuming step).
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In the current work, we implement the meshless local radial point interpolation (MLRPI) method to find numerical solution of one-dimensional linear telegraph equations with variable coefficients. The MLRPI method, as a meshless technique, does not require any background More
In the current work, we implement the meshless local radial point interpolation (MLRPI) method to find numerical solution of one-dimensional linear telegraph equations with variable coefficients. The MLRPI method, as a meshless technique, does not require any background integration cells and all integrations are carried out locally over small quadrature domains of regular shapes, such as lines in one dimensions, circles or squares in two dimensions and spheres or cubes in three dimensions. Weak form formulation of the discretized equations has been constructed on local subdomains, hence the domain and boundary integrals in the weak form methods can easily be evaluated over the regularly shaped subdomains by some numerical quadratures. Radial basis functions augmented with monomials are used in to create shape functions. These shape functions have delta function property. Also the time derivatives is eliminated by using two-step finite differences approximation. Two illustrative numerical examples are given to show the stability and accuracy of the present method.
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‎This article is devoted to study the weak solutions of a class of nonlinear system of fractional boundary value problems including both Volterra and Fredholm linear integral terms. This system of fractional semi-linear Fredholm-Volterra integro-differential equatio More
‎This article is devoted to study the weak solutions of a class of nonlinear system of fractional boundary value problems including both Volterra and Fredholm linear integral terms. This system of fractional semi-linear Fredholm-Volterra integro-differential equations does have a gradient of a nonlinear source term as well. We apply the critical point theory and the variational structure to prove the existence of at least three distinct weak solutions to the system. Furthermore, it is presented an example to verify the legitimacy and applicability of the ‎theory.‎
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In this letter, the problem of determining heat transfer from convecting-radiating fin of rectangular shape is investigated. We consider steady conduction in the fin and neglect radiative exchange between adjacent fins and between the fin and its primary surface. It is More
In this letter, the problem of determining heat transfer from convecting-radiating fin of rectangular shape is investigated. We consider steady conduction in the fin and neglect radiative exchange between adjacent fins and between the fin and its primary surface. It is demonstrated that the governing fin equation is exactly solvable. The exact, closed-form analytical solutions in implicit form are convenient for physical interpretation and optimization for maximum heat transfer.
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The convergence of thisiterative sequence is then controlled by an embedded parameter. The fastest convergence occurs for an optimal embedded parameter which maximizes a special function. This optimization problem brings a sequence with high rate of the convergence to t More
The convergence of thisiterative sequence is then controlled by an embedded parameter. The fastest convergence occurs for an optimal embedded parameter which maximizes a special function. This optimization problem brings a sequence with high rate of the convergence to theunique solution in the finite region where $\frac{\partial f}{\partial y}$ has to be positive.Some illustrative examples are given to confirm the validity and reliability of this constructive theory.
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This work presents the generalized nonlinear multi-terms fractional variable-order differential equation with proportional delays. In this paper, a novel shifted Jacobi operational matrix technique is introduced to solve a class of these equations mentioned, so that the More
This work presents the generalized nonlinear multi-terms fractional variable-order differential equation with proportional delays. In this paper, a novel shifted Jacobi operational matrix technique is introduced to solve a class of these equations mentioned, so that the main problem becomes a system of algebraic equations that we can solve numerically. The suggested technique is successfully developed for the aforementioned problem. Comprehensive numerical tests are provided to demonstrate the generality, efficiency, accuracy of presented scheme and the flexibility of this technique. The numerical experiments compared it with other existing methods such as Reproducing Kernel Hilbert Space method ($ RKHSM $). Comparing the results of these methods as well as comparing the current method ($NSJOM$) with the true solution, indicating the validity and efficiency of this scheme. Note that the procedure is easy to implement and this technique will be considered as a generalization of many numerical schemes. Furthermore, the error and its bound are estimated.
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