Name : Final Exam Practice Problems : Professor : Paul J . Atzberger Partial Differential Equations , 124 A March 11 th , 2007

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Computational technique of linear partial differential equations by reduced differential transform ‎method

This paper presents a class of theoretical and iterative method for linear partial differential equations. An algorithm and analytical solution with a initial condition is obtained using the reduced differential transform method. In this technique, the solution is calculated in the form of a series with easily computable components. There test modeling problems from mathematical mechanic, physi...

Spatially adaptive stochastic numerical methods for intrinsic fluctuations in reaction-diffusion systems

Stochastic partial differential equations are introduced for the continuum concentration fields of reaction-diffusion systems. The stochastic partial differential equations account for fluctuations arising from the finite number of molecules which diffusively migrate and react. Spatially adaptive stochastic numerical methods are developed for approximation of the stochastic partial differential...

At the Interface of Math and

Paul Atzberger, a professor in UCSB's Department of Mathematics and in mechanical engineering. In popular culture, mathematics is often deemed inaccessible or esoteric. Yet in the modern world, it plays an ever more important role in our daily lives and a decisive role in the discovery and development of new ideas — often behind the scenes.

Application of the tan(phi/2)-expansion method for solving some partial differential equations

In this paper, the improved  -expansion method is proposed to solve the Kundu–Eckhaus equation and Gerdjikov–Ivanov model. The applied method are analytical methods to obtaining the exact solutions of nonlinear equations. Here, the aforementioned methods are used for constructing the soliton, periodic, rational, singular and solitary wave solutions for solving some equations. We obtained furthe...