Abstract
In this paper, we generalize the recently developed Finite Integration Method (FIM) for the solutions of high-dimensional partial differential equations. Formulation of this Generalized Finite Integration Method (GFIM) can be derived due to the use of piecewise polynomials in the numerical integrations. The GFIM does not require the strict requirement for uniformly distributed nodal points in the original FIM. This robustness advantage extends the applicability of FIM to solve partial differential equations by using direct Kronecker product. Due to the unconditional stability of numerical integrations, the GFIM is effective and efficient to solve higher dimensional partial differential equations with stiffness. For numerical verification, we construct several 1D to 4D problems with different types of stiffness and make comparisons among existing numerical methods.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
