فهرس المقالات Spectral method

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  1 - Numerical Study of Unsteady Flow of Gas Through a Porous Medium By Means of Chebyshev Pseudo-Spectral Method
  S. M. Hosseini Herat E. Babolian S. Abbasbandy
  In this work, we first reformulate the unsteady flow of gas through a porous medium problem in [0,+∞) to a problem in [-1,1] by variable transformation μ = (x-s)/(x+s), and using spectral collocation method based on Chebyshev polynomials to approximate the resu أکثر

  In this work, we first reformulate the unsteady flow of gas through a porous medium problem in [0,+∞) to a problem in [-1,1] by variable transformation μ = (x-s)/(x+s), and using spectral collocation method based on Chebyshev polynomials to approximate the resulting problem. The comparison of the results obtained by this method with results obtained by other methods shows that this method provides more accurate and numerically stable solutions. تفاصيل المقالة
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  2 - Construction of ‎P‎seudospectral Meshless Radial Point Interpolation for Sobolev Equation with Error Analysis‎
  S. Abbasbandy E. Shivanian
  10.30495/ijim.2022.19382
  In this study, we develop an approximate formulation for two-dimensional (2D) Sobolev equations based on pseudospectral meshless radial point interpolation (PSMRPI). The Sobolev equations which are arisen in the fluid flow penetrating rocks, soils, or different viscous أکثر

  In this study, we develop an approximate formulation for two-dimensional (2D) Sobolev equations based on pseudospectral meshless radial point interpolation (PSMRPI). The Sobolev equations which are arisen in the fluid flow penetrating rocks, soils, or different viscous media do not have an exact solution except in some special cases. The problem can be rigorously solved particularly when the geometry of the domain is more complex. In the PSMRPI method, the nodal points do not need to be regularly distributed and can even be quite arbitrary. It is easy to have high order derivatives of unknowns in terms of the values at nodal points by constructing operational matrices. It is proved that the method is convergent and unconditionally stable in some sense with respect to the time. The main results of the Sobolev equation are demonstrated by some examples to show the validity and trustworthiness of the PSMRPI technique. تفاصيل المقالة
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  3 - An Improvement on Collocation Algorithm to Solve Initial Value Problems
  M. Nikarya S. Sarabadan
  10.30495/ijim.2022.17794.873
  In this paper an improved version of the collocation method is proposed to solve ordinary differential equations with initial conditions. Our proposed algorithm is described by applying it to some well-known IVPs. The results are compared with basic collocation algorith أکثر

  In this paper an improved version of the collocation method is proposed to solve ordinary differential equations with initial conditions. Our proposed algorithm is described by applying it to some well-known IVPs. The results are compared with basic collocation algorithms to show the advantages, applicability and efficiency of the proposed method. Based on numerical results, the proposed algorithm has better accuracy and execution time. تفاصيل المقالة
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  4 - The spectral iterative method for Solving Fractional-Order Logistic ‎Equation
  A. Shoja‎ E. Babolian A. R. Vahidi
  In this paper, a new spectral-iterative method is employed to give approximate solutions of fractional logistic differential equation. This approach is based on combination of two different methods, i.e. the iterative method \cite{35} and the spectral method. The method أکثر

  In this paper, a new spectral-iterative method is employed to give approximate solutions of fractional logistic differential equation. This approach is based on combination of two different methods, i.e. the iterative method \cite{35} and the spectral method. The method reduces the differential equation to systems of linear algebraic equations and then the resulting systems are solved by a numerical method. The solutions obtained are compared with Adomian decomposition method and iterative method used in \cite{35‎} and Adams method \cite{36}.‎ تفاصيل المقالة
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  5 - Elastic Buckling of Moderately Thick Homogeneous Circular Plates of Variable Thickness
  S.K Jalali M.H Naei
  In this study, the buckling response of homogeneous circular plates with variable thickness subjected to radial compression based on the first-order shear deformation plate theory in conjunction with von-Karman nonlinear strain-displacement relations is investigated. Fu أکثر

  In this study, the buckling response of homogeneous circular plates with variable thickness subjected to radial compression based on the first-order shear deformation plate theory in conjunction with von-Karman nonlinear strain-displacement relations is investigated. Furthermore, optimal thickness distribution over the plate with respect to buckling is presented. In order to determine the distribution of the prebuckling load along the radius, the membrane equation is solved using the shooting method. Subsequently, employing the pseudospectral method that makes use of Chebyshev polynomials, the stability equations are solved. The influence of the boundary conditions, the thickness variation profile and aspect ratio on the buckling behavior is examined. The comparison shows that the results derived, using the current method, compare very well with those available in the literature. تفاصيل المقالة
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  6 - Spectral Scheme for Solving Fuzzy Volterra Integral Equations of First Kind
  Laleh Hooshangian
  This paper discusses about the solution of fuzzy Volterra integral equation of first-kind (F-VIE1) using spectral method. The parametric form of fuzzy driving term is applied for F-VIE1, then three classifications for (F-VIE1) are searched to solve them. These classific أکثر

  This paper discusses about the solution of fuzzy Volterra integral equation of first-kind (F-VIE1) using spectral method. The parametric form of fuzzy driving term is applied for F-VIE1, then three classifications for (F-VIE1) are searched to solve them. These classifications are considered based on the interval sign of the kernel. The Gauss-Legendre points and Legendre weights for arithmetics in spectral method are used to solve (F-VIE1). Finally, two examples are got to illustrate more. However, accuracy and efficiency are shown in tables. \ تفاصيل المقالة
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  7 - Spectral method for Solving Fuzzy Volterra Integral Equations of Second kind
  Laleh Hooshangian
  This paper, about the solution of fuzzy Volterra integral equation of fuzzy Volterra integral equation of second kind (F-VIE2) using spectral method is discussed. The parametric form of fuzzy driving term is applied for F-VIE2. Then three cases for (F-VIE2) are searched أکثر

  This paper, about the solution of fuzzy Volterra integral equation of fuzzy Volterra integral equation of second kind (F-VIE2) using spectral method is discussed. The parametric form of fuzzy driving term is applied for F-VIE2. Then three cases for (F-VIE2) are searched to solve them. This classifications are considered based on the sign of interval. The Gauss-Legendre points and Legendre weights for arithmetics in spectral method are used to solve (F-VIE2). Finally two examples are got to illustrate more.b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b تفاصيل المقالة
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  8 - A Legendre-spectral scheme for solution of nonlinear system of Volterra-Fredholm integral equations
  L. Hooshangian D. Mirzaie
  This paper gives an ecient numerical method for solving the nonlinear systemof Volterra-Fredholm integral equations. A Legendre-spectral method based onthe Legendre integration Gauss points and Lagrange interpolation is proposedto convert the nonlinear integral equatio أکثر

  This paper gives an ecient numerical method for solving the nonlinear systemof Volterra-Fredholm integral equations. A Legendre-spectral method based onthe Legendre integration Gauss points and Lagrange interpolation is proposedto convert the nonlinear integral equations to a nonlinear system of equationswhere the solution leads to the values of unknown functions at collocationpoints. تفاصيل المقالة
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  9 - Numerical Optimal Control of The Wave Equation
  Hassan Zarei Ali Zafari
  In this paper, we present a spectral method for approximating the boundary optimal control problems of a well-known wave equation by the linear optimal control problems. The method is based upon constructing the Mth degree interpolation polynomials, using Chebyshevs nod أکثر

  In this paper, we present a spectral method for approximating the boundary optimal control problems of a well-known wave equation by the linear optimal control problems. The method is based upon constructing the Mth degree interpolation polynomials, using Chebyshevs nodes, to approximate the wave equation. Necessary conditions for optimal control functions are obtained by using the Pontryagin's maximum principle. Moreover, the control parameterization enhancing technique (CPET) is used to obtain the piecewise constant sub-optimal control functions. Finally, the efficiency of the proposed method is confirmed by a numerical example. تفاصيل المقالة
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  10 - Numerical solution of Fredholm and Volterra integral equations using the normalized Müntz−Legendre polynomials
  فرشته صائمی حمیده ابراهیمی محمود شفیعی
  The current research approximates the unknown function based on the normalized Müntz−Legendre polynomials (NMLPs) in conjunction with a spectral method for the solution of nonlinear Fredholm and Volterra integral equations. In this method, by using operationa أکثر

  The current research approximates the unknown function based on the normalized Müntz−Legendre polynomials (NMLPs) in conjunction with a spectral method for the solution of nonlinear Fredholm and Volterra integral equations. In this method, by using operational matrices, a system of algebraic equations is derived that can be readily handled through the use of the Newton scheme. The stability, error bound, and convergence analysis of the method are discussed in detail by preparing some theorems. Several illustrative examples are provided formally to show the efficiency of the proposed method. تفاصيل المقالة