Convergence of a random walk method for a partial differential equation

Convergence of a random walk method for a partial differential equation

A Cauchy problem for a one–dimensional diffusion–reaction equation is solved on a grid by a random walk method, in which the diffusion part is solved by random walk of particles, and the (nonlinear) reaction part is solved via Euler’s polygonal arc method. Unlike in the literature, we do not assume monotonicity for the initial condition. It is proved that the algorithm converges and the rate of...

Convergence of a Random Walk Method for the Burgers Equation

We show that the solution of the Burgers equation can be approximated in LX(R), to within 0(m~1/*(lnm)2), by a random walk method generated by 0(m) particles. The nonlinear advection term of the equation is approximated by advecting the particles in a velocity field induced by the particles. The diffusive term is approximated by adding an appropriate random perturbation to the particle position...

Solving Fuzzy Partial Differential Equation by Differential Transformation Method

  Normal 0 false false false ...

Exact solutions of a linear fractional partial differential equation via characteristics method

‎In recent years‎, ‎many methods have been studied for solving differential equations of fractional order‎, ‎such as Lie group method, ‎invariant subspace method and numerical methods‎, ‎cite{6,5,7,8}‎. Among this‎, ‎the method of characteristics is an efficient and practical method for solving linear fractional differential equations (FDEs) of multi-order‎. In this paper we apply this method f...

A method for solving first order fuzzy differential equation