A Qualocation Method for Parabolic Partial Integro-Differential Equations in One Space Variable
In this article, a qualocation method is formulated and analyzed for parabolic partial integro-differential equations in one space variable. Using a new Ritz–Volterra type projection, optimal rates of convergence are derived. Based on the second-order backward differentiation formula, a fully discrete scheme is formulated and a convergence analysis is derived. Results of numerical experiments are presented which support the theoretical results.
The authors gratefully acknowledge the research support of the Department of Science and Technology, Government of India, through the National Programme on Differential Equations: Theory, Computation and Applications, DST Project No.SERB/F/1279/2011-2012. LPT acknowledges the support through Institute Post-Doctoral Fellowship of IIT-Bombay. Support was also received by GF from IIT Bombay while a Distinguished Guest Professor at that institution. The authors wish to thank the referees for their insightful comments and constructive suggestions, which significantly improved the manuscript.
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