Should I take partial differential equations?
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| Papers (7) | Insight |
|---|---|
31 Citations | The used methods present a wider applicability for handling the nonlinear partial differential equations. |
96 Citations | We can also be solved other couple system of partial differential equations by this new technique. |
27 Citations | This paper reports a novel technique of forming improved finite-difference solutions of partial differential equations. |
59 Citations | This paper presents an observation that under reasonable conditions, many partial differential equations from mathematical physics possess three structural properties. |
16 Citations | The new approach can be directly applied to other partial differential equations. |
64 Citations | Being concise and straightforward, the calculations demonstrate the effectiveness and convenience of the method for solving other nonlinear partial differential equations. |
70 Citations | The results obtained confirm that the proposed method is an efficient technique for analytic treatment of a wide variety of nonlinear systems of partial differential equations. |
Related Questions
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Are there any higher-order in time and NOT in space partial differential equations?5 answersYes, there are higher-order accurate time discretizations discussed in the literature, such as the higher-order accurate time implicit Discontinuous Galerkin (DG) discretizations presented in Min Goo Lee's dissertation. Additionally, the proposal of a higher-order approximation for Caputo fractional derivatives for time fractional partial differential equations is another example of higher-order methods in time. These approaches focus on achieving higher accuracy in the time domain while maintaining lower-order accuracy in the spatial domain. The utilization of graded mesh and central difference approximations for time derivatives showcases the advancement in time discretization techniques. These methods highlight the importance of enhancing temporal accuracy in solving partial differential equations while keeping spatial discretization at a lower order.
RBF methods for solving partial differential equations?4 answersRBF methods have been used to solve nonlinear partial differential equations (PDEs) by reducing the equations to a time-discrete form and transforming them into a system of algebraic equations using radial basis functions (RBFs). Multilevel augmented local RBF-FD algorithms have been developed to enhance the convergence rate of the RBF-FD scheme for solving PDEs. Padua points, a type of RBF distribution, have been used in three-dimensional space to solve PDEs with high accuracy and low computational costs. A new global RBF method called coupled radial basis function (CRBF) has been proposed, which achieves accurate and stable numerical solutions independent of the shape parameter values. RBF partition of unity collocation method based on a finite difference scheme has been used for the numerical solution of time-dependent stochastic PDEs, providing stability and low computational cost.
What is partial differential equation?5 answersA partial differential equation (PDE) is a type of differential equation where the unknown function depends on two or more variables. PDEs are used to represent physical processes and are solved analytically or numerically to examine the behavior of the system. They are widely used in physics, mathematics, engineering, and other fields. PDEs can model phenomena such as diffusion, advection, and random movement of particles. Numerical methods are often used to solve PDEs when analytic solutions are not feasible. These methods provide an alternative tool for finding solutions under prescribed initial conditions. The accuracy and applicability of numerical methods for solving PDEs have been demonstrated in various studies.
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