About the Nonlinear Galerkin Method

Use

• A nonlinear Galerkin method is the process by which inertial manifolds are utilized to reduce any spacial errors present in Galerkin equations. The equation is run parallel to the standard Galerkin method to identity the errors in the original formula. This process is done to identify evolutional differential equations through time and space. The nonlinear Galerkin method also is used in industrial settings to determine the fatigue or fail rate of machinery.

Formula

• The nonlinear Galerkin is q(t) ͭ6; φ(p(t)), yt + Ay + P N(y + φ(y)) = 0, z(t) = y(t) + φ(y(t). The letters in the formula stand for the different questions presenting in the equation, such as the rate of speed the object runs, the trajectory of an object, the time involved and initial inertia. The formula for each specific equation is slightly different due to the individual measurements for each letter. Not all nonlinear Galerkin equations contain the same information.

Process

• The nonlinear Galerkin method is plugged into the equation using all of the above formulas and information. The method determines the flat manifold of the object. The equation is then compared with the information gathered from the original Galerkin formula so that errors are easily visible. If done on a computer, the entire process takes only a few seconds to complete.

Benefits

• The benefits of using nonlinear Galerkin methods to verify information and view potential errors are numerous. With these equations, it is possible to see the exact expected lifetime for a given object or scenario. The nonlinear Galerkin method can also identify errors in the original equation, ensuring that incorrect formulas and solutions are not used as final data results or interpretations.