Nonlinear Equations with N-dimensional Telegraph Operator Iterated K-times
نویسنده
چکیده
In this article, using distribution kernel, we study the nonlinear equations with n-dimensional telegraph operator iterated k-times. Keywords—Telegraph operator, Elementary solution, Distribution
منابع مشابه
A new block by block method for solving two-dimensional linear and nonlinear Volterra integral equations of the first and second kinds
In this paper, we propose a new method for the numerical solution of two-dimensional linear and nonlinear Volterra integral equations of the first and second kinds, which avoids from using starting values. An existence and uniqueness theorem is proved and convergence isverified by using an appropriate variety of the Gronwall inequality. Application of the method is demonstrated for solving the ...
متن کاملOn the Generalized Nonlinear Diamond Heat Kernel
In this paper, we study the nonlinear heat equation ∂ ∂t △u(x, t) − c♦u(x, t) = f(x, t, u(x, t)), where△k is the Laplacian operator iterated k− times and is defined by (1.4)and ♦k is the Diamond operator iterated k− times and is defined by (1.2). We obtain an interesting kernel related to the nonlinear heat equation.
متن کاملOn the Vector Process Obtained by Iterated Integration of the Telegraph Signal
We analyse the vector process (X0(t), X1(t), . . . , Xn(t), t > 0) where Xk(t) = t ∫ 0 Xk−1(s)ds, k = 1, . . . , n, and X0(t) is the two-valued telegraph process. In particular, the hyperbolic equations governing the joint distributions of the process are derived and analysed. Special care is given to the case of the process (X0(t), X1(t), X2(t), t > 0) representing a randomly accelerated motio...
متن کاملThe Discrete Galerkin Method for Nonlinear Integral Equations
Let K be a completely continuous nonlinear integral operator, and consider solving x = K(x) by Galerkin's method. This can be written as xn = PnK(xn),Pn an orthogonal projection; the iterated Galerkin solution is defined by xn = K(xn). We give a general framework and error analysis for the numerical method that results from replacing all integrals in Galerkin's method with numerical integrals. ...
متن کاملChebyshev Spectral Collocation Method for Computing Numerical Solution of Telegraph Equation
In this paper, the Chebyshev spectral collocation method(CSCM) for one-dimensional linear hyperbolic telegraph equation is presented. Chebyshev spectral collocation method have become very useful in providing highly accurate solutions to partial differential equations. A straightforward implementation of these methods involves the use of spectral differentiation matrices. Firstly, we transform ...
متن کامل