Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: , exploiting the quadratic spline collocation (QSC) method,  numerically solve the time fractional subdiffusion equation with Dirichelt boundary value conditions. The coefficient matrix of the discretized linear system is investigated in detail. Theoretical analyses and numerical examples demonstrate the proposed technique can enjoy the global error bound with O ( ? 3 + h 3 ) under the L∞ norm provided that the solution v(x, t) has four-order continual derivative with respects to x and t, and it can achieve the accuracy of O ( ? 4 + h 4 ) at collocation points, where ?, h are the step sizes in time and space, respectively.
['Wei-Hua Luo', 'Ting-Zhu Huang', 'Guo-Cheng Wu', 'Xian-Ming Gu']
I am writing a research paper on a idea Quadratic spline collocation method for the time fractional subdiffusion equation
[{"from": "human", "value": "I am writing a research paper on a idea Quadratic spline collocation method for the time fractional subdiffusion equation"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: , exploiting the quadratic spline collocation (QSC) method,  numerically solve the time fractional subdiffusion equation with Dirichelt boundary value conditions. The coefficient matrix of the discretized linear system is investigated in detail. Theoretical analyses and numerical examples demonstrate the proposed technique can enjoy the global error bound with O ( ? 3 + h 3 ) under the L\u221e norm provided that the solution v(x, t) has four-order continual derivative with respects to x and t, and it can achieve the accuracy of O ( ? 4 + h 4 ) at collocation points, where ?, h are the step sizes in time and space, respectively."}]