A New Numerical Method for Time Fractional Non-linear Sharma-Tasso-Oliver Equation and Klein-Gordon Equation With Exponential Kernel Law
Frontiers in Physics, ISSN: 2296-424X, Vol: 8
2020
- 11Citations
- 5Captures
Metric Options: Counts1 Year3 YearSelecting the 1-year or 3-year option will change the metrics count to percentiles, illustrating how an article or review compares to other articles or reviews within the selected time period in the same journal. Selecting the 1-year option compares the metrics against other articles/reviews that were also published in the same calendar year. Selecting the 3-year option compares the metrics against other articles/reviews that were also published in the same calendar year plus the two years prior.
Example: if you select the 1-year option for an article published in 2019 and a metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019. If you select the 3-year option for the same article published in 2019 and the metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019, 2018 and 2017.
Citation Benchmarking is provided by Scopus and SciVal and is different from the metrics context provided by PlumX Metrics.
Example: if you select the 1-year option for an article published in 2019 and a metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019. If you select the 3-year option for the same article published in 2019 and the metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019, 2018 and 2017.
Citation Benchmarking is provided by Scopus and SciVal and is different from the metrics context provided by PlumX Metrics.
Article Description
In this work, we derived a novel numerical scheme to find out the numerical solution of fractional PDEs having Caputo-Fabrizio (C-F) fractional derivatives. We first find out the formula of approximation for the C-F derivative of the function f(t) = t. We approximate the C-F derivative in time direction with the help of Legendre spectral method and approximation formula of t. The unknown function and their derivatives in spatial direction are approximated with the help of the method which is based on a quasi wavelet. We implement this newly derived method to solve the non-linear Sharma-Tasso-Oliver equation and non-linear Klein-Gordon equation in which time-fractional derivative is of C-F type. The accuracy and validity of this new method are depicted by giving the numerical solution of some numerical examples. The numerical results for the particular cases of Klein-Gordon equation are compared with the existing exact solutions and from the obtained error we can conclude that our proposed numerical method achieves accurate results. The effect of time-fractional exponent α on the solution profile is characterized by figures. The comparison of solution profile u(x, t) for different type time-fractional derivative (C-F vs. Caputo) is depicted by figures.
Bibliographic Details
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=85085316337&origin=inward; http://dx.doi.org/10.3389/fphy.2020.00136; https://www.frontiersin.org/article/10.3389/fphy.2020.00136/full; https://dx.doi.org/10.3389/fphy.2020.00136; https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2020.00136/full
Frontiers Media SA
Provide Feedback
Have ideas for a new metric? Would you like to see something else here?Let us know