pdeDomain1D

pdeDomain1D(xGrid)

Defines the spatial domain and grid discretization for solving one-dimensional partial differential equations (PDEs).

When solving PDEs numerically, the continuous spatial domain must first be discretized into separate nodes. pdeDomain1D wraps the specified node vector (xGrid) into a domain object that can be recognized by the solver pdeSolver.

Main use cases:

• Defining computational boundaries: determine the physical range to solve over from the start and end points of the grid.

• Controlling computational accuracy: use a denser grid in regions with rapid changes, such as near the strike price in option pricing, and a sparser grid in smoother regions to balance speed and accuracy.

xGrid A numeric vector that specifies all computational nodes in space.

• The nodes must be valid finite numeric values and must not contain NULL, NaN, or Inf. They must be strictly increasing.

• It must contain at least 3 points. Generally, more points produce a more accurate numerical solution, but also increase computation time.

• The range of the grid (the difference between the maximum and minimum values) must be finite.

• You can use the pdeGrid1D function to construct the nodes.

Returns a dictionary containing the following fields:

• type: STRING scalar, fixed to "structured1D".

• dim: INT scalar, fixed to 1.

• xGrid: DOUBLE vector, the normalized spatial node vector.

Note: Grid statistics, such as the number of nodes, spacing, and uniformity, are not directly included in the returned dictionary. Use pdeInfo(domain) to query them.

Example 1. Construct a uniform one-dimensional grid

// Construct a uniform grid from 0 to 1 with 101 nodes
xGrid = (0..100) / 100.0
domain = pdeDomain1D(xGrid)

Example 2. Construct a non-uniform one-dimensional grid

// Manually specify non-uniformly distributed nodes
xGrid = 0.0 0.05 0.15 0.4 1.0
domain = pdeDomain1D(xGrid)

Example 3. Use with pdeGrid1D

// Use the sinh method to refine the grid around 100
spotGrid = pdeGrid1D(0.0, 300.0, 401, "sinh", 100.0, 3.0)
domain = pdeDomain1D(spotGrid)

Related Functions: pdeGrid1D, pdeInfo, pdeSolver