Abstract
A method is presented for finding the solution of deterministic partial differential equations at an arbitrary point of the domain of definition of these equations referred to as the local solution. The method is based on the Ito calculus, properties of diffusion processes, and Monte Carlo simulation. The theoretical background of the proposed method is relatively difficult. However, the method has attractive features for applications. For example, the numerical algorithms based on the proposed method are simple, stable, accurate, local, and ideal for parallel computation. Numerical examples from mechanics are presented to demonstrate the use and the accuracy of the proposed method.
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