[PDF] Top 20 Numerical Solution of a Nonlinear Integro-Differential Equation

... Navier-Stokes equation, which serves to the production of a velocity field corresponding to thermal fluctuations [4, 5], or by a turbulent velocity field with Kolmogorov scaling behavior [6], was studied by three of ... See full document

... . This yields an equation based on the unknown which is the ap- proximation u x   . To examine the accuracy of the for- mula, we present some examples. We will show the dif- ference between the accurate and ... See full document

... fractional differential transform method [4, 30], sinc-collocation method [3, 12], Laplace transform method [20, 22] and least squares method ...But, numerical solution of functional fractional ... See full document

... The disadvantage of the explicit method in terms of the nonlinear neural model is the severe constraint in the size of the coefficient of the second spatial derivative, K. As K increases, the time step used for ... See full document

... reduced differential transform method was applied to obtain the exact solution of linear and nonlinear Schrodinger ...analytical solution of linear and nonlinear partial ... See full document

... The method of solving higher-order ODEs by reducing them to a system of first-order equation involves more functions evaluation which to evaluate leads to computational burden as mentioned in (Master, 2011) and ... See full document

... Since G(t, s) >0 and f : I × K × K ® K is continuous, Q : C(I, K) ® C(I, K) is contin- uous. Obviously, a positive solution of the boundary value problem (1) and (3) is equivalent to a nonzero fixed point of ... See full document

... exact solution to be y(x) = x 2 + x. Table 3 shows the numerical results including absolute errors of the approxi- mated solution by using composite trapezoidal rule and number of iterations k = ... See full document

... Many mathematical modelings of various physical phenomena contain FIDEs [6, 11, 36]. Generally speaking, the analytical solutions of most FIDEs are not easy to obtain. Therefore, seeking numerical solutions of ... See full document

... trivial solution of the former ...trivial solution of that (VIDE). Our conditions involve the nonlinear generalization and extensions of those found in the ... See full document

... In Section 2, a brief review of TFs and fractional calculus is presented. In Section 3, operational matrices of TFs for fractional integration are derived. Section 4 is devoted to the formulation of system of fractional ... See full document

... In [8], two dimensional DTM is used to solve partial differential equations (PDEs). In [9], one dimensional DTM is applied to solve linear and nonlinear initial value problems. In [10], one and two ... See full document

... fuzzy differential equations plays an important role in modelling of science and engineering problems because this theory represents a natural way to model dynamical systems under ...fuzzy differential ... See full document

... Saeid Moloudzadeh was born in the Naghadeh-Iran in 1976. He re- ceived B.Sc degree in mathematics and M.Sc degree in applied mathe- matics from Payam-e-Noor Univer- sity of Naghadeh, science and re- search Branch, IAU to ... See full document

... stability Solution . for another system of non-linear integro-differential equations of Volterra type Consider the following system of non-linear integro-differential equations which ... See full document

... the solution of systems of convolution-type Volterra integral equations of the first kind, In: Inverse problems for differential equations of the mathematical physics (Russian), Novasibirsk: ...Faires, ... See full document

... Abstract: In this paper, the concept of Successive Approximation method also called the Picard Iteration Method (PIM) for solving Fractional integro-differential equations is introduced. The fractional ... See full document

... Definition 1.[5]. A continuous function 𝑓 satisfy a Lipschitz condition on the domain 𝐺 = {(𝑡, 𝑥): 𝑎 ≤ 𝑡 ≤ 𝑏, 𝑐 ≤ 𝑥 ≤ 𝑑} in the variable 𝑥 on 𝐺 if for all 𝐾 > 0 and (𝑡, 𝑥 1 ), (𝑡, 𝑥 2 ) ∈ 𝐺 , such that |𝑓(𝑡, 𝑥 1 ) − ... See full document

... and integro-differential equations, because a great number of problems in physi- cal science and engineering are modeled by such equations [6, 5, 2, 15, 11, 13, 16, 17, 9, 3, 10, 4, ...for numerical ... See full document

... Volterra integro-differential equations are usually difficult to solve in an analytical ...and numerical treatment see for instance 2–15 for the classical methods and recent ...our numerical method as ... See full document