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What kind of numerical method does 'pdepe' (MATLAB function's) use?

I'm using the MATLAB's function 'pdepe' to solve a problem with some partial differential equations, a parabolic one.

I need to know the kind of numerical method that function uses, 'cause I have to notify this in a report.

The description of the function in MathWorks is "Solve initial-boundary value problems for systems of parabolic and elliptic PDEs in one space variable and time". Is it a finite difference method?

Thanks for helping me.

Solution

  • Taken from the Matlab 2016b documentation for pdepe:

    The time integration is done with ode15s. pdepe exploits the capabilities of ode15s for solving the differential-algebraic equations that arise when Equation 1-3 contains elliptic equations, and for handling Jacobians with a specified sparsity pattern.

    Also, from the ode15s documentation:

    ode15s is a variable-step, variable-order (VSVO) solver based on the numerical differentiation formulas (NDFs) of orders 1 to 5. Optionally, it can use the backward differentiation formulas (BDFs, also known as Gear's method) that are usually less efficient